Electric Force Between Spheres Doubled Separation

(I) What is the magnitude of the electric force of attraction between an iron nucleus \((q=+26 e)\) and its innermost electron if the distance between them is \(1.5 \times 10^{-12} \mathrm{~m} ?\) Equation Transcription: Text Transcription: (q=+26e) 1.5 times 10^-12 m

(I) How many electrons make up a charge of \(-48.0 \mu \mathrm{C}\) ? Equation Transcription: Text Transcription: -48.0 mu C

(I) What is the magnitude of the force a \(+25 \mu \mathrm{C}\) charge exerts on a \(+2.5 \mathrm{mC}\) charge 16 cm away? Equation Transcription: Text Transcription: +25 mu C +2.5 mC

(I) What is the repulsive electrical force between two protons \(4.0 \times 10^{-15} \mathrm{~m}\) apart from each other in an atomic nucleus? Equation Transcription: Text Transcription: 4.0 times 10^-15 m

(II) When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is \(3.0 \mu \mathrm{C}\), by what percentage does the mass of a 9.0-g comb change during charging? Equation Transcription: Text Transcription: 3.0 mu C

(II) Two charged dust particles exert a force of \(4.2 \times 10^{-2} \mathrm{~N}\) on each other. What will be the force if they are moved so they are only one-eighth as far apart? Equation Transcription: Text Transcription: 4.2 times 10^-2 N

Two small charged spheres are 6.52 cm apart. They are moved, and the force each exerts on the other is found to have tripled. How far apart are they now

(II) A person scuffing her feet on a wool rug on a dry day accumulates a net charge of \(-28 \mu \mathrm{C}\). How many excess electrons does she get, and by how much does her mass increase? Equation Transcription: Text Transcription: -28 mu C

What is the total charge of all the electrons in a 12-kg bar of gold? What is the net charge of the bar? (Gold has 79 electrons per atom and an atomic mass of 197 u

(II) Compare the electric force holding the electron in orbit \(\left(r=0.53 \times 10^{-10} \mathrm{~m}\right)\) around the proton nucleus of the hydrogen atom, with the gravitational force between the same electron and proton. What is the ratio of these two forces? Equation Transcription: Text Transcription: (r=0.53 times 10^-10 m)

(II) Particles of charge \(+65,+48\), and \(-95 \mu \mathrm{C}\) are placed in a line (Fig. 16-52). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two. Equation Transcription: Text Transcription: +65,+48, -95 mu C

(II) Three positive particles of equal charge, \(+17.0 \mu \mathrm{C}\) are located at the corners of an equilateral triangle of side 15.0 cm (Fig. 16–53). Calculate the magnitude and direction of the net force on each particle due to the other two. Equation Transcription: Text Transcription: +17.0 mu C

A charge Q is transferred from an initially uncharged plastic ball to an identical ball 24 cm away. The force of attraction is then 17 mN. How many electrons were transferred from one ball to the other?

A charge of 6.15 mC is placed at each corner of a square 0.100 m on a side. Determine the magnitude and direction of the force on each charge

(II) At each corner of a square of side \(\ell\) there are point charges of magnitude \(Q, 2Q, 3Q,\) and \(4Q\) (Fig. 16–54). Determine the magnitude and direction of the force on the charge \(2Q\). Equation Transcription: ? Text Transcription: ell Q, 2Q,3Q,4Q 2Q

(II) A large electroscope is made with “leaves” that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26° angle with the vertical (Fig. 16–55), what total charge Q must have been applied to the electroscope? Ignore the mass of the wires.

(III) Two small nonconducting spheres have a total charge of \(90.0 \mu \mathrm{C}\). (a ) When placed 28.0 cm apart, the force each exerts on the other is 12.0 N and is repulsive. What is the charge on each? (b) What if the force were attractive? Equation Transcription: Text Transcription: 90.0 mu C

(III) Two charges, \(-Q\) and \(-3 Q\), are a distance \(\ell\) apart. These two charges are free to move but do not because there is a third (fixed) charge nearby. What must be the magnitude of the third charge and its placement in order for the first two to be in equilibrium? Equation Transcription: ? Text Transcription: -Q -3Q ell

(I) Determine the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2460 N/C that points due east.

(I) A proton is released in a uniform electric field, and it experiences an electric force of \(1.86 \times 10^{-14} \mathrm{~N}\) toward the south. Find the magnitude and direction of the electric field. Equation Transcription: Text Transcription: 1.86 times 10^-14 N

(I) Determine the magnitude and direction of the electric field 21.7 cm directly above an isolated \(33.0 \times 10^{-6} \mathrm{C}\) charge. Equation Transcription: Text Transcription: 33.0 times 10^-6 C

(I) A downward electric force of 6.4 N is exerted on a \(-7.3 \mu \mathrm{C}\) charge. Find the magnitude and direction of the electric field at the position of this charge. Equation Transcription: Text Transcription: -7.3 mu C

(II) Determine the magnitude of the acceleration experienced by an electron in an electric field of 756 N/C. How does the direction of the acceleration depend on the direction of the field at that point?

(II) Determine the magnitude and direction of the electric field at a point midway between a \(-8.0 \mu \mathrm{C}\) and a \(+5.8 \mu \mathrm{C}\) charge 6.0 cm apart. Assume no other charges are nearby. Equation Transcription: Text Transcription: -8.0 mu C +5.8 mu C

(II) Draw, approximately, the electric field lines about two point charges, \(+Q\) and \(-3 Q\), which are a distance \(\ell\) apart. Equation Transcription: ? Text Transcription: +Q, -3Q ell

(II) What is the electric field strength at a point in space where a proton experiences an acceleration of 2.4 million " g 's"?

(II) An electron is released from rest in a uniform electric field and accelerates to the north at a rate of \(105 \mathrm{~m} / \mathrm{s}^{2}\). Find the magnitude and direction of the electric field. Equation Transcription: Text Transcription: 105 m/s^2

(II) The electric field midway between two equal but opposite point charges is 386 N/C, and the distance between the charges is 16.0 cm. What is the magnitude of the charge on each?

(II) Calculate the electric field at one corner of a square 1.22 m on a side if the other three corners are occupied by \(3.25 \times 10^{-6} \mathrm{C}\) charges. Equation Transcription: Text Transcription: 3.25 times 10^-6 C

(II) Calculate the electric field at the center of a square 42.5 cm on a side if one corner is occupied by a \(-38.6 \mu \mathrm{C}\) charge and the other three are occupied by \(-27.0 \mu \mathrm{C}\) charges. Equation Transcription: Text Transcription: -38.6 mu C -27.0 mu C

II) Determine the direction and magnitude of the electric field at the point P in Fig. 16-56. The charges are separated by a distance \(2 a\), and point P is a distance \(x\) from the midpoint between the two charges. Express your answer in terms of \(Q, x, a\), and \(k\). Equation Transcription: Text Transcription: 2a x Q,x,a,k

(II) Two point charges, \(Q_{1}=-32 \ \mu \mathrm C\) and \(Q_{2}=+45 \ \mu \mathrm C\), are separated by a distance of 12 cm.The electric field at the point P (see Fig. 16-57) is zero. How far from is \(Q_1\) P?

(II) Determine the electric field \(\overrightarrow{\mathbf{E}}\) at the origin 0 in Fig. 16-58 due to the two charges at A and B. Equation Transcription: Text Transcription: overrightarrow^E

(II) You are given two unknown point charges, \(Q_{1}\) and \(Q_{2}\). At a point on the line joining them, one-third of the way from \(Q_{1}\) to \(Q_{2}\), the electric field is zero (Fig. 16-59). What is the ratio \(Q_{1} / Q_{2}\) ? Equation Transcription: Text Transcription: Q_1 Q_2 Q_1 Q_2 Q_1/Q_2

(III) Use Coulomb's law to determine the magnitude and direction of the electric field at points A and B in Fig. 16-60 due to the two positive charges \((Q=4.7 \mu \mathrm{C})\) shown. Are your results consistent with Fig. 16-32b? Equation Transcription: Text Transcription: (Q=4.7 mu C)

(III) An electron (mass \(m=9.11 \times 10^{-31} \mathrm{~kg}\) ) is accelerated in the uniform field \(\overrightarrow{\mathbf{E}}\) \(\left(E=1.45 \times 10^{4} \mathrm{~N} / \mathrm{C}\right)\) between two thin parallel charged plates. The separation of the plates is 1.60 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate, Fig. 16-61. (a) With what speed does it leave the hole? (b) Show that the gravitational force can be ignored. Equation Transcription: Text Transcription: m=9.11 times 10^-31 kg overrightarrow^ E(E=1.45 times 10^4 N/C)

(III) The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in Fig. 16-39. Assume that the net average charge (due to electron sharing) indicated on H and N atoms has magnitude \(0.2 e\) and on the indicated C and O atoms is \(0.4 e\). Assume also that atoms on each molecule are separated by \(1.0 \times 10^{-10} \mathrm{~m}\). Estimate the net force between (a) a thymine and an adenine; and (b) a cytosine and a guanine. For each bond (red dots) consider only the three atoms in a line (two atoms on one molecule, one atom on the other). (c) Estimate the total force for a DNA molecule containing \(10^{5}\) pairs of such molecules. Assume half are A-T pairs and half are C-G pairs. Equation Transcription: Text Transcription: 0.2e 0.4e 1.0 times 10^-10 m 10^5

(I) The total electric flux from a cubical box of side 28.0 cm is \(1.85 \times 10^{3} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}\). What charge is enclosed by the box? Equation Transcription: Text Transcription: 1.85 times 10^3 N cdot m^2/C

(II) In Fig. 16-62, two objects, \(\mathrm{O}_{1}\) and \(\mathrm{O}_{2}\), have charges \(+1.0 \mu \mathrm{C}\) and \(-2.0 \mu \mathrm{C}\), respectively, and a third object, \(\mathrm{O}_{3}\), is electrically neutral. (a) What is the electric flux through the surface \(A_{1}\) that encloses all three objects? (b) What is the electric flux through the surface \(A_{2}\) that encloses the third object only? Equation Transcription: Text Transcription: O_1 O_2 +1.0 mu C -2.0 mu C A_1 A_2

(II) A cube of side 8.50 cm is placed in a uniform field \(E=7.50 \times 10^{3} \mathrm{~N} / \mathrm{C}\) with edges parallel to the field lines. (a) What is the net flux through the cube? (b) What is the flux through each of its six faces? Equation Transcription: Text Transcription: E=7.50 times 10^3 N/C

(II) The electric field between two parallel square metal plates is 130 N/C The plates are 0.85 m on a side and are separated by 3.0 cm. What is the charge on each plate (assume equal and opposite)? Neglect edge effects.

(II) The field just outside a 3.50-cm radius metal ball is \(3.75 \times 10^{2} \mathrm{~N} / \mathrm{C}\) and points toward the ball. What charge resides on the ball? Equation Transcription: Text Transcription: 3.75 times 10^2 N/C

A point charge Q rests at the center of an uncharged thin spherical conducting shell. (See Fig. 1634.) What is the electric field E as a function of r (a) for r less than the inner radius of the shell, (b) inside the shell, and (c) beyond the shell? (d) How does the shell affect the field due to Q alone? How does the charge Q affect the shell?

How close must two electrons be if the magnitude of the electric force between them is equal to the weight of either at the Earths surface?

Given that the human body is mostly made of water, estimate the total amount of positive charge in a 75-kg person

A 3.0-g copper penny has a net positive charge of \(32 \mu \mathrm{C}\). What fraction of its electrons has it lost? Equation Transcription: Text Transcription: 32 mu C

Measurements indicate that there is an electric field surrounding the Earth. Its magnitude is about 150 N/C at the Earth's surface and points inward toward the Earth's center. What is the magnitude of the electric charge on the Earth? Is it positive or negative? [Hint: The electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at its center.]

(a) The electric field near the Earth's surface has magnitude of about 150 N/C. What is the acceleration experienced by an electron near the surface of the Earth? (b) What about a proton? (c) Calculate the ratio of each acceleration to \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\). Equation Transcription: Text Transcription: g=9.8 m/s^2

A water droplet of radius 0.018 mm remains stationary in the air. If the downward-directed electric field of the Earth is 150 N/C, how many excess electron charges must the water droplet have?

Estimate the net force between the CO group and the HN group shown in Fig. 16-63. The C and O have charges \(\pm 0.40 e\), and the H and N have charges \(\pm 0.20 e\), where \(e=1.6 \times 10^{-19} \mathrm{C}\). [Hint: Do not include the "internal" forces between C and O or between H and N.] Equation Transcription: Text Transcription: pm 0.40e pm 0.20e e=1.6 times 10^-19 C

In a simple model of the hydrogen atom, the electron revolves in a circular orbit around the proton with a speed of \(2.2 \times 10^{6} \mathrm{~m} / \mathrm{s}\). Determine the radius of the electron's orbit. [Hint: See Chapter 5 on circular motion.] Equation Transcription: Text Transcription: 2.2 times 10^6 m/s

Two small charged spheres hang from cords of equal length \(\ell\) as shown in Fig. 16-64 and make small angles \(\theta_{1}\) and \(\theta_{2}\) with the vertical. (a) If \(Q_{1}=Q, Q_{2}=2 Q\), and \(m_{1}=m_{2}=m\), determine the ratio \(\theta_{1} / \theta_{2}\). (b) Estimate the distance between the spheres. Equation Transcription: ? Text Transcription: ell theta_1 theta_2 Q_1=Q, Q_2=2Q m_1=m_2=m theta_1\theta_2

A positive point charge \(Q_{1}=2.5 \times 10^{-5} \mathrm{C}\) is fixed at the origin of coordinates, and a negative point charge \(Q_{2}=-5.0 \times 10^{-6} \mathrm{C}\) is fixed to the \(x\) axis at \(x=+2.4 \mathrm{~m}\). Find the location of the place(s) along the \(x\) axis where the electric field due to these two charges is zero. Equation Transcription: Text Transcription: Q_1=2.5 times 10^-5 C QQ_2=-5.0 times 10^-6 C x x=+2.4 m x

Dry air will break down and generate a spark if the electric field exceeds about \(3 \times 10^{6} \mathrm{~N} / \mathrm{C}\). How much charge could be packed onto a green pea (diameter 0.75 cm ) before the pea spontaneously discharges? [Hint: Eqs. 16-4 work outside a sphere if is measured from its center.] Equation Transcription: Text Transcription: 3 times 10^6 N/C

Two point charges, \(Q_{1}=-6.7 \mu \mathrm{C}\) and \(Q_{2}=1.8 \mu \mathrm{C}\), are located between two oppositely charged parallel plates, as shown in Fig. 16-65. The two charges are separated by a distance of \(x=0.47 \mathrm{~m}\). Assume that the electric field produced by the charged plates is uniform and equal to \(E=53,000 \mathrm{~N} / \mathrm{C}\). Calculate the net electrostatic force on \(Q_{1}\) and give its direction. Equation Transcription: Text Transcription: Q_1=-6.7 mu C Q_2=1.8 mu C x=0.47 m E=53,000 N/C Q_1

Packing material made of pieces of foamed polystyrene can easily become charged and stick to each other. Given that the density of this material is about \(35 \mathrm{~kg} / \mathrm{m}^{3}\), estimate how much charge might be on a 2.0-cm-diameter foamed polystyrene sphere, assuming the electric force between two spheres stuck together is equal to the weight of one sphere. Equation Transcription: Text Transcription: 35 kg/m^3

A point charge \((m=1.0\) gram ) at the end of an insulating cord of length 55 cm is observed to be in equilibrium in a uniform horizontal electric field of 9500 N/C, when the pendulum's position is as shown in Fig. 16-66, with the charge 12 cm above the lowest (vertical) position. If the field points to the right in Fig. 16–66, determine the magnitude and sign of the point charge. Equation Transcription: Text Transcription: m=1.0

Two small, identical conducting spheres A and B are a distance R apart; each carries the same charge Q. (a) What is the force sphere B exerts on sphere A? (b) An identical sphere with zero charge, sphere C, makes contact with sphere B and is then moved very far away. What is the net force now acting on sphere A? (c) Sphere C is brought back and now makes contact with sphere A and is then moved far away. What is the force on sphere A in this third case?

For an experiment, a colleague of yours says he smeared toner particles uniformly over the surface of a sphere 1.0 m in diameter and then measured an electric field of 5000 N/C near its surface. (a) How many toner particles (Example 16–6) would have to be on the surface to produce these results? (b) What is the total mass of the toner particles?

A proton \(\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)\) is suspended at rest in a uniform electric field \(\overrightarrow{\mathbf{E}}\). Take into account gravity at the Earth's surface, and determine \(\overrightarrow{\mathbf{E}}\). Equation Transcription: Text Transcription: (m=1.67 times 10^-27 kg) overrightarrow^E overrightarrow^E

A point charge of mass 0.185 kg, and net charge \(+0.340 \mu C\), hangs at rest at the end of an insulating cord above a large sheet of charge. The horizontal sheet of fixed uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the cord is measured to be 5.18 N. Calculate the magnitude and direction of the electric field due to the sheet of charge (Fig. 16–67).

An electron with speed \(v_{0}=5.32 \times 10^{6} \mathrm{~m} / \mathrm{s}\) is traveling parallel to an electric field of magnitude \(E=9.45 \times 10^{3} \mathrm{~N} / \mathrm{C}\). (a) How far will the electron travel before it stops? (b) How much time will elapse before it returns to its starting point? Equation Transcription: Text Transcription: v_0=5.32 times 10^6 m/s E=9.45 times 10^3 N/C

Given the two charges shown in Fig. 16–68, at what position(s) \(x\) is the electric field zero? Equation Transcription: Text Transcription: x

What is the total charge of all the electrons in a 25-kg bar of aluminum? (Aluminum has 13 electrons per atom and an atomic mass of 27 u.)

Two point charges, \(+Q\) and \(-Q\) of mass \(m\), are placed on the ends of a massless rod of length \(\ell\), which is fixed to a table by a pin through its center. If the apparatus is then subjected to a uniform electric field \(E\) parallel to the table and perpendicular to the rod, find the net torque on the system of rod plus charges. Equation Transcription: ? Text Transcription: +Q -Q ell E

Determine the direction and magnitude of the electric field at point P, Fig. 16-69. The two charges are separated by a distance of \(2 a\). Point P is on the perpendicular bisector of the line joining the charges, a distance \(x\) from the midpoint between them. Express your answers in terms of \(Q, x, a\), and \(k\). Equation Transcription: Text Transcription: 2a x Q,x,a,k

A mole of carbon contains \(7.22 \times 10^{24}\) electrons. Two electrically neutral carbon spheres, each containing 1 mole of carbon, are separated by 15.0 cm (center to center). What fraction of electrons would have to be transferred from one sphere to the other for the electric force and the gravitational force between the spheres to be equal? Equation Transcription: Text Transcription: 7.22 times 10^24

Problem 1COQ Two identical tiny spheres have the same electric charge. If their separation is doubled, the force each exerts on the other will be (a) half. (b) double. (c) four times larger. (d) one-quarter as large. (e) unchanged.

\(Q_{1}=0.10 \mu C\) is located at the origin. \(Q_{2}=+0.10 \mu C\) is located on the positive x axis at x = 1.0 m. Which of the following is true of the force on due to ? (a) It is attractive and directed in the +x direction. (b) It is attractive and directed in the -x direction. (c) It is repulsive and directed in the +x direction. (d) It is repulsive and directed in the -x direction. Equation transcription” Text transcription: Q{1}=0.10 mu C Q{2}=+0.10 mu C

Problem 1P (I) What is the magnitude of the electric force of attraction between an iron nucleus (q =+26e) and its innermost electron if the distance between them is 1.5 X 10-12 m?

Problem 1Q If you charge a pocket comb by rubbing it with a silk scarf, how can you determine if the comb is positively or negatively charged?

Problem 1SL Referring to Section 16–4 and Figs. 16–11 and 16–12, what happens to the separation of the leaves of an electroscope when the charging object is removed from an electroscope (a) charged by induction and (b) charged by conduction? (c) Is it possible to tell whether the electroscope in Fig. 16–12a has been charged by induction or by conduction? If so, which way was it charged? (d) Draw electric field lines (Section 16–8) for the electroscopes in Figs. 16–11a and 16–11b, omitting the fields around the charging rod. How do the fields differ?

Problem 2MCQ Swap the positions of Q1 and Q2 of MisConceptual Question 1. Which of the following is true of the force on Q1 due Q2 to? (a) It does not change. (b) It changes from attractive to repulsive. (c) It changes from repulsive to attractive. (d) It changes from the +x direction to the –x direction. (e) It changes from the –x direction to the +x direction.

Problem 2P (I) How many electrons make up a charge of -48.0 µC?

Problem 2Q Why does a shirt or blouse taken from a clothes dryer sometimes cling to your body?

Problem 2SL Four equal positive point charges, each of charge 6.4 ?C are at the corners of a square of side 9.2 cm. What charge should be placed at the center of the square so that all charges are at equilibrium? Is this a stable or an unstable equilibrium (Section 9–4) in the plane?

Fred the lightning bug has a mass m and a charge +q. Jane, his lightning-bug wife, has a mass of \(\frac{3}{4}\)m and a charge -2q. Because they have charges of opposite sign, they are attracted to each other. Which is attracted more to the other, and by how much? (a) Fred, twice as much. (b) Jane, twice as much. (c) Fred, four times as much. (d) Jane, four times as much. (e) They are attracted to each other by the same amount. Equation transcription: Text transcription: frac{3}{4}

Problem 3P (I) What is the magnitude of the force a +25 µC charge exerts on a +2.5 mC charge 16 cm away?

Problem 3Q Explain why fog or rain droplets tend to form around ions or electrons in the air.

Suppose electrons enter a uniform electric field midway between two plates at an angle \(\theta_{0}\) to the horizontal, as shown in Fig. 16-70. The path is symmetrical, so they leave at the same angle \(\theta_{0}\) and just barely miss the top plate. What is \(\theta_{0}\)? Ignore fringing of the field. Equation transcription: Text transcription: theta{0}

4. Figure 16-50 shows electric field lines due to a point charge. What can you say about the field at point 1 compared with the field at point (a) The field at point 2 is larger, because point 2 is on a field line. (b) The field at point 1 is larger, because point 1 is not on a field line. (c) The field at point 1 is zero, because point 1 is not on a field line. (d) The field at point 1 is larger, because the field lines are closer together in that region.

Problem 4P (I) What is the repulsive electrical force between two protons 4.0 X 10-15 m apart from each other in an atomic nucleus?

Problem 4Q Why does a plastic ruler that has been rubbed with a cloth have the ability to pick up small pieces of paper? Why is this difficult to do on a humid day?

Problem 4SL What experimental observations mentioned in the text rule out the possibility that the numerator in Coulomb’s law contains the sum (Q1 +Q2) rather than the product Q1 Q2 ?

A negative point charge is in an electric field created by a positive point charge. Which of the following is true? (a) The field points toward the positive charge, and the force on the negative charge is in the same direction as the field. (b) The field points toward the positive charge, and the force on the negative charge is in the opposite direction to the field. (c) The field points away from the positive charge, and the force on the negative charge is in the same direction as the field. (d) The field points away from the positive charge, and the force on the negative charge is in the opposite direction to the field.

Problem 5P (II) When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is 3.0 µC, by what percentage does the mass of a 9.0-g comb change during charging?

Problem 5Q A positively charged rod is brought close to a neutral piece of paper, which it attracts. Draw a diagram showing the separation of charge in the paper, and explain why attraction occurs.

Problem 5SL Near the surface of the Earth, there is a downward electric field of 150 N/C and a downward gravitational field of 9.8 N/kg A charged 1.0-kg mass is observed to fall with acceleration 8.0 m/s2 .What are the magnitude and sign of its charge?

Problem 6MCQ As an object acquires a positive charge, its mass usually (a) decreases. (b) increases. (c) stays the same. (d) becomes negative.

Problem 6P (II) Two charged dust particles exert a force of 4.2 X 10-2 N on each other. What will be the force if they are moved so they are only one-eighth as far apart?

Problem 6Q Contrast the net charge on a conductor to the “free charges” in the conductor.

Problem 6SL Identical negative charges (Q =-e) are located at two of the three vertices of an equilateral triangle. The length of a side of the triangle is l What is the magnitude of the net electric field at the third vertex? If a third identical negative charge was located at the third vertex, then what would be the net electrostatic force on it due to the other two charges? Use symmetry and explain how you used it.

Problem 7MCQ Refer to Fig. 16–32d. If the two charged plates were moved until they are half the distance shown without changing the charge on the plates, the electric field near the center of the plates would (a) remain almost exactly the same. (b) increase by a factor of 2. (c) increase, but not by a factor of 2. (d) decrease by a factor of 2. (e) decrease, but not by a factor of 2.

Problem 7P (II) Two small charged spheres are 6.52 cm apart. They are moved, and the force each exerts on the other is found to have tripled. How far apart are they now?

Figures 16–7 and 16–8 show how a charged rod placed near an uncharged metal object can attract (or repel) electrons. There are a great many electrons in the metal, yet only some of them move as shown. Why not all of them?

Problem 7SL Suppose that electrical attraction, rather than gravity, were responsible for holding the Moon in orbit around the Earth. If equal and opposite charges Q were placed on the Earth and the Moon, what should be the value of Q to maintain the present orbit? Use data given on the inside front cover of this book. Treat the Earth and Moon as point particles.

We wish to determine the electric field at a point near a positively charged metal sphere (a good conductor). We do so by bringing a small positive test charge, \(q_{0}\), to this point and measure the force \(F_{0}\) on it. \(F_{0} / q_{0}\) will be the electric field \(\vec{E}\) as it was at that point before the test charge was present. (a) greater than (b) less than (c) equal to Equation transcription: Text transcription: F{0} Q{0} F{0} / q{0} vec{E}

Problem 8P (II) A person scuffing her feet on a wool rug on a dry day accumulates a net charge of -28µC. How many excess electrons does she get, and by how much does her mass increase?

Problem 8Q When an electroscope is charged, its two leaves repel each other and remain at an angle. What balances the electric force of repulsion so that the leaves don’t separate further?

Problem 9MCQ We are usually not aware of the electric force acting between two everyday objects because (a) the electric force is one of the weakest forces in nature. (b) the electric force is due to microscopic-sized particles such as electrons and protons. (c) the electric force is invisible. (d) most everyday objects have as many plus charges as minus charges.

The balloon in Fig. 16–48 was rubbed on a student’s hair. Explain why the water drip curves instead of falling vertically.

Problem 10MCQ To be safe during a lightning storm, it is best to be (a) in the middle of a grassy meadow. (b) inside a metal car. (c) next to a tall tree in a forest. (d) inside a wooden building. (e) on a metal observation tower.

Problem 10P (II) Compare the electric force holding the electron in orbit (r =0.53 X 10-10 m) around the proton nucleus of the hydrogen atom, with the gravitational force between the same electron and proton. What is the ratio of these two forces?

Problem 10Q The form of Coulomb’s law is very similar to that for Newton’s law of universal gravitation. What are the differences between these two laws? Compare also gravitational mass and electric charge.

Problem 11MCQ Which are the worst places in MisConceptual Question 10?

(II) Particles of charge \(+65,+48\), and \(-95 \mu C\) are placed in a line (Fig. 16-52). The center one is from each of the others. Calculate the net force on each charge due to the other two. Equation transcription: Text transcription: +65,+48 -95 mu C

Problem 11Q When a charged ruler attracts small pieces of paper, sometimes a piece jumps quickly away after touching the ruler. Explain.

Which vector best represents the direction of the electric field at the fourth corner of the square due to the three charges shown in Fig. 16–51?

(II) Three positive particles of equal charge, \(+17.0 \mu C\), are located at the corners of an equilateral triangle of side 15.0 cm (Fig. 16–53). Calculate the magnitude and direction of the net force on each particle due to the other two. Equation transcription: Text transcription: +17.0 mu C

Problem 12Q We are not normally aware of the gravitational or electric force between two ordinary objects. What is the reason in each case? Give an example where we are aware of each one and why.

Problem 13MCQ A small metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positively charged rod held near the ball. The charge of the ball must be (a) positive. (b) negative. (c) neutral. (d) positive or neutral. (e) negative or neutral.

Problem 13P (II) A charge Q is transferred from an initially uncharged plastic ball to an identical ball 24 cm away. The force of attraction is then 17 mN. How many electrons were transferred from one ball to the other?

Problem 13Q Explain why the test charges we use when measuring electric fields must be small.

Problem 14P (II) A charge of 6.15 mC is placed at each corner of a square 0.100 m on a side. Determine the magnitude and direction of the force on each charge.

Problem 14Q When determining an electric field, must we use a positive test charge, or would a negative one do as well? Explain.

(II) At each corner of a square of side \(\ell\) there are point charges of magnitude Q, 2Q, 3Q, and 4Q (Fig. 16-54). Determine the magnitude and direction of the force on the charge 2Q.

Problem 15Q Draw the electric field lines surrounding two negative electric charges a distance apart.

Return to the Chapter-Opening Question, page 443, and answer it again now. Try to explain why you may have answered differently the first time.

In Example 16–2, how is the direction of \(F_{12}\) related to the direction of \(F_{21}\)? Equation transcription: Text transcription: F{12} F{21}

Determine the magnitude and direction of the net force on charge \(Q_{2}\) in Fig. 16–19a. Equation transcription: Text transcription: Q{2}

In Example 16–5, what distance must \(Q_{4}\) be from \(Q_{3}\)? Equation transcription: Text transcription: Q{4} Q{3}

Problem 16EE (a) Consider two point charges, +Q and -Q which are fixed a distance d apart. Can you find a location where a third positive charge Q could be placed so that the net electric force on this third charge is zero? (b) What if the first two charges were both +Q?

Find the magnitude and direction of the electric field due to a \(-2.5\ \mu C\) charge 50 cm below it.

Problem 16EG Four charges of equal magnitude, but possibly different sign, are placed on the corners of a square. What arrangement of charges will produce an electric field with the greatest magnitude at the center of the square? (a) All four positive charges; (b) all four negative charges; (c) three positive and one negative; (d) two positive and two negative; (e) three negative and one positive.

(II) A large electroscope is made with "leaves" that are 78 -cm-long wires with tiny spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a angle with the vertical (Fig. 16-55), what total charge must have been applied to the electroscope? Ignore the mass of the wires.

Assume that the two opposite charges in Fig. 16–32a are 12.0 cm apart. Consider the magnitude of the electric field 2.5 cm from the positive charge. On which side of this charge—top, bottom, left, or right—is the electric field the strongest? The weakest? Explain.

Problem 17P (III) Two small nonconducting spheres have a total charge Of 90.0µC. (a) When placed 28.0 cm apart, the force each exerts on the other is 12.0 N and is repulsive. What is the charge on each? (b) What if the force were attractive?

Consider the electric field at the three points indicated by the letters A, B, and C in Fig. 16–49. First draw an arrow at each point indicating the direction of the net force that a positive test charge would experience if placed at that point, then list the letters in order of decreasing field strength (strongest first). Explain.

Problem 18P (III) Two charges, -Q and -Q are a distance l apart. These two charges are free to move but do not because there is a third (fixed) charge nearby. What must be the magnitude of the third charge and its placement in order for the first two to be in equilibrium?

Why can electric field lines never cross?

Problem 19Q Show, using the three rules for field lines given in Section 16–8, that the electric field lines starting or ending on a single point charge must be symmetrically spaced around the charge.

Problem 19P (I) Determine the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2460 N/C that points due east.

Problem 20P (I) A proton is released in a uniform electric field, and it experiences an electric force of 1.86 X 10-14N toward the south. Find the magnitude and direction of the electric field.

Problem 20Q Given two point charges, Q and 2Q, a distance l apart, is there a point along the straight line that passes through them where E = 0 when their signs are (a) opposite, (b) the same? If yes, state roughly where this point will be.

Problem 21P (I) Determine the magnitude and direction of the electric field 21.7 cm directly above an isolated 33.0 X 10-6 charge.

Problem 22P (I) A downward electric force of 6.4 N is exerted on a -7.3 µC charge. Find the magnitude and direction of the electric field at the position of this charge.

Consider a small positive test charge located on an electric field line at some point, such as point P in Fig. 16–32a. Is the direction of the velocity and/or acceleration of the test charge along this line? Discuss.

Problem 22Q A point charge is surrounded by a spherical gaussian surface of radius r. If the sphere is replaced by a cube of side r, will ?E be larger, smaller, or the same? Explain.

Problem 23P (II) Determine the magnitude of the acceleration experienced by an electron in an electric field of 756 N/C How does the direction of the acceleration depend on the direction of the field at that point?

Problem 24P (II) Determine the magnitude and direction of the electric field at a point midway between a -8.0 µC and a +5.8 µC charge 6.0 cm apart. Assume no other charges are nearby.

Problem 25P (II) Draw, approximately, the electric field lines about two point charges, ±Q and –3Q, which are a distance l apart.

Problem 26P (II) What is the electric field strength at a point in space where a proton experiences an acceleration of 2.4 million “g’s”?

Problem 27P (II) An electron is released from rest in a uniform electric field and accelerates to the north at a rate of 105 m/s2. Find the magnitude and direction of the electric field.

Problem 28P (II) The electric field midway between two equal but opposite point charges is 386 N/C and the distance between the charges is 16.0 cm. What is the magnitude of the charge on each?

Problem 29P (II) Calculate the electric field at one corner of a square 1.22 m on a side if the other three corners are occupied by 3.25 X 10-6 charges.

Problem 30P (II) Calculate the electric field at the center of a square 42.5 cm on a side if one corner is occupied by a -38.6 µC charge and the other three are occupied by -27.0 µC charges.

Problem 31P (II) Determine the direction and magnitude of the electric field at the point P in Fig. 16–56. The charges are separated by a distance 2a, and point P is a distance x from the midpoint between the two charges. Express your answer in terms of Q, x, a, and k.

(II) Two point charges, \(Q_{1}=-32 \mu C\) and \(Q_{2}=+45 \mu C\), are separated by a distance of . The electric field at the point (see Fig. 16-57) is zero. How far from is ? Equation transcription: Text transcription: Q{1}=-32 mu C Q{2}=+45 mu C

(II) Determine the electric field \(\vec{E}\) at the origin 0 in Fig. 16-58 due to the two charges at A and B. Equation transcription: Text transcription: vec{E}

(II) You are given two unknown point charges, \(Q_{1}\) and \(Q_{2}\). At a point on the line joining them, one-third of the way from \(Q_{1}\) to \(Q_{2}\), the electric field is zero (Fig. 16-59). What is the ratio \(Q_{1} / Q_{2}\)? Equation transcription: Text transcription: Q{1} Q{2} Q{1} / Q{2}

(III) Use Coulomb's law to determine the magnitude and direction of the electric field at points and in Fig. 16-60 due to the two positive charges \((Q=4.7 \mu C)\) shown. Are your results consistent with Fig. 16-32b? Equation transcription: Text transcription: (Q=4.7 mu C)

(III) An electron (mass \(m=9.11 \times 10^{-31} k g\) ) is acceler-ated in the uniform field \(\vec{E}\) \(\left(E=1.45 \times 10^{4} N / C\right)\) between two thin parallel charged plates. The separation of the plates is . The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate, Fig. 16-61. (a) With what speed does it leave the hole? (b) Show that the gravitational force can be ignored. Equation transcription: Text transcription: m=9.11 times 10^{-31} k g vec{E} (E=1.45 times 10^{4} N / C)

Problem 37P (III) The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in Fig. 16–39. Assume that the net average charge (due to electron sharing) indicated on H and N atoms has magnitude 0.2e and on the indicated C and O atoms is 0.4e. Assume also that atoms on each molecule are separated by 1.0 X 10-10 m. Estimate the net force between (a) a thymine and an adenine; and (b) a cytosine and a guanine. For each bond (red dots) consider only the three atoms in a line (two atoms on one molecule, one atom on the other). (c) Estimate the total force for a DNA molecule containing 105 pairs of such molecules. Assume half are A–T pairs and half are C–G pairs.

Problem 38P (I) The total electric flux from a cubical box of side 28.0 cm 1.85 X 103 N.m2/C. is What charge is enclosed by the box?

(II) In Fig. 16-62, two objects, \(O_{1}\) and \(\mathrm{O}_{2}\), have charges \(+1.0 \mu C\) and \(-2.0 \mu C\), respectively, and a third object, \(\mathrm{O}_{3}\), is electrically neutral. (a) What is the electric flux through the surface \(A_{1}\) that encloses all three objects? ( ) What is the electric flux through the surface \(A_{2}\) that encloses the third object only? Equation transcription: Text transcription: O{1} {O}{2} +1.0 mu C -2.0 mu C {O}_{3} A{1} A{2}

Problem 40P (II) A cube of side 8.50 cm is placed in a uniform field E =7.50 X 103 N/C with edges parallel to the field lines. (a) What is the net flux through the cube? (b) What is the flux through each of its six faces?

Problem 41P (II) The electric field between two parallel square metal plates is 130 N/C. The plates are 0.85 m on a side and are separated by 3.0 cm. What is the charge on each plate (assume equal and opposite)? Neglect edge effects.

Problem 43P (III) A point charge Q rests at the center of an uncharged thin spherical conducting shell. (See Fig. 16–34.) What is the electric field E as a function of r (a) for r less than the inner radius of the shell, (b) inside the shell, and (c) beyond the shell? (d) How does the shell affect the field due to Q alone? How does the charge Q affect the shell?

Problem 42P (II) The field just outside a 3.50-cm-radius metal ball is 3.75 X 102 N/C and points toward the ball. What charge resides on the ball?

Problem 44GP How close must two electrons be if the magnitude of the electric force between them is equal to the weight of either at the Earth’s surface?

Problem 45GP Given that the human body is mostly made of water, estimate the total amount of positive charge in a 75-kg person.

Problem 46GP Measurements indicate that there is an electric field surrounding the Earth. Its magnitude is about 150 N/C at the Earth’s surface and points inward toward the Earth’s center. What is the magnitude of the electric charge on the Earth? Is it positive or negative? [Hint: The electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at its center.]

Problem 47GP Measurements indicate that there is an electric field surrounding the Earth. Its magnitude is about 150 N/C at the Earth’s surface and points inward toward the Earth’s center. What is the magnitude of the electric charge on the Earth? Is it positive or negative? [Hint: The electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at its center.]

Problem 48GP (a) The electric field near the Earth’s surface has magnitude of about 150 N/C. What is the acceleration experienced by an electron near the surface of the Earth? (b) What about a proton? (c) Calculate the ratio of each acceleration to g=9.8 m/s2

Problem 49GP A water droplet of radius 0.018 mm remains stationary in the air. If the downward-directed electric field of the Earth is 150 N/C, how many excess electron charges must the water droplet have?

Estimate the net force between the CO group and the HN group shown in Fig. 16-63. The and have charges \(\pm 0.40 e\), and the and have charges \(\pm 0.20 e\), where \(e=1.6 \times 10^{-19} \mathrm{C}\). [Hint: Do not include the "internal" forces between and , or between and .] Equation transcription: Text transcription: pm 0.40 e pm 0.20 e e=1.6 times 10^{-19} C}

Problem 51GP In a simple model of the hydrogen atom, the electron revolves in a circular orbit around the proton with a speed of 2.2*106 m/s. Determine the radius of the electron’s orbit. [Hint: See Chapter 5 on circular motion.]

Two small charged spheres hang from cords of equal length as shown in Fig. 16-64 and make small angles \(\theta_{1}\) and \(\theta_{2}\) with the vertical. If \(Q_{1}=Q, Q_{2}=2 Q\), and \(m_{1}=m_{2}=m\) determine the ratio \(\theta_{1} / \theta_{2}\) (b) Estimate the distance between the spheres. Equation transcription: Text transcription: theta{1} theta{2} Q{1}=Q, Q{2}=2 Q m{1}=m{2}=m theta{1} / theta{2}

.A positive point charge \(Q_{1}=2.5 \times 10^{-5} \mathrm{C}\) is fixed at the origin of coordinates, and a negative point charge \(Q_{2}=-5.0 \times 10^{-6} \mathrm{C}\) is fixed to the axis at \(x=+2.4 m\) Find the location of the place(s) along the axis where the electric field due to these two charges is zero. Equation transcription: Text transcription: Q{1}=2.5 times 10^{-5}{C} Q{2}=-5.0 times 10^{-6}{C} x=+2.4 m

Problem 54GP Dry air will break down and generate a spark if the electric field exceeds about 3*106 N/C. How much charge could be packed onto a green pea (diameter 0.75 cm) before the pea spontaneously discharges? [Hint: Eqs. 16–4 work outside a sphere if r is measured from its center.]

Two point charges, \(Q_{1}=-6.7 \mu C\) and \(Q_{2}=1.8 \mu \mathrm{C}\), are located between two oppositely charged parallel plates, as shown in Fig. 16-65. The two charges are separated by a distance of \(x=0.47 \mathrm{~m}\). Assume that the electric field produced by the charged plates is uniform and equal to . Calculate the net electrostatic force on \(Q_{1}\) and give its direction. Equation transcription: Text transcription: Q{1}=-6.7 mu C Q{2}=1.8 mu{C} x=0.47{~m} Q{1}

Problem 56GP Packing material made of pieces of foamed polystyrene can easily become charged and stick to each other. Given that the density of this material is about 35 kg/m3, estimate how much charge might be on a 2.0-cm-diameter foamed polystyrene sphere, assuming the electric force between two spheres stuck together is equal to the weight of one sphere.

A point charge gram at the end of an insulating cord of length is observed to be in equilibrium in a uniform horizontal electric field of , when the pendulum's position is as shown in Fig. , with the charge above the lowest charge above the lowest (vertical) position. If the field points to the right in Fig. , determine the magnitude and sign of the point charge.

Problem 58GP Two small, identical conducting spheres A and B are a distance R apart; each carries the same charge Q. (a) What is the force sphere B exerts on sphere A? (b) An identical sphere with zero charge, sphere C, makes contact with sphere B and is then moved very far away. What is the net force now acting on sphere A? (c) Sphere C is brought back and now makes contact with sphere A and is then moved far away. What is the force on sphere A in this third case?

Problem 59GP For an experiment, a colleague of yours says he smeared toner particles uniformly over the surface of a sphere 1.0 m in diameter and then measured an electric field of 5000 N/C near its surface. (a) How many toner particles (Example 16–6) would have to be on the surface to produce these results? (b) What is the total mass of the toner particles?

A proton \(\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)\) is suspended at rest in a uniform electric field \(\(\vec{E}\)\). Take into account gravity at the Earth's surface, and determine \(\vec{E}\). Equation transcription: Text transcription: (m=1.67 times 10^{-27}{~kg}) vec{E}

A point charge of mass , and net charge \(+0.34 \mu C\), hangs at rest at the end of an insulating cord above a large sheet of charge. The horizontal sheet of fixed uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the cord is measured to be . Calculate the magnitude and direction of the electric field due to the sheet of charge (Fig. 16-67). Equation transcription: Text transcription: +0.34 mu C

An electron with speed \(v_{0}=5.32 x 10^{6} m / s\) is traveling parallel to an electric field of magnitude \(E=9.45 \times 10^{3} N / C\). (a) How far will the electron travel before it stops? (b) How much time will elapse before it returns to its starting point? Equation transcription: Text transcription: v{0}=5.32 x 10^{6} m / s E=9.45 times 10^{3} N / C

Given the two charges shown in Fig. 16-68, at what position(s) is the electric field zero?

Problem 64GP What is the total charge of all the electrons in a 25-kg bar of aluminum? (Aluminum has 13 electrons per atom and an atomic mass of 27 u.)

Problem 65GP Two point charges, +Q and -Q of mass m, are placed on the ends of a massless rod of length l, which is fixed to a table by a pin through its center. If the apparatus is then subjected to a uniform electric field E parallel to the table and perpendicular to the rod, find the net torque on the system of rod plus charges.

Determine the direction and magnitude of the electric field at point P, Fig. 16-69. The two charges are separated by a distance of . Point is on the perpendicular bisector of the line joining the charges, a distance from the midpoint between them. Express your answers in terms of , and .

Problem 67GP A mole of carbon contains 7.22*1024 electrons. Two electrically neutral carbon spheres, each containing 1 mole of carbon, are separated by 15.0 cm (center to center). What fraction of electrons would have to be transferred from one sphere to the other for the electric force and the gravitational force between the spheres to be equal?

What is the magnitude of the electric force of attraction between an iron nucleus and its innermost electron if the distance between them is

How many electrons make up a charge of 48.0 mC?

What is the magnitude of the force a charge exerts on a charge 16 cm away?

What is the repulsive electrical force between two protons apart from each other in an atomic nucleus?

When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is by what percentage does the mass of a 9.0-g comb change during charging?

Two charged dust particles exert a force of 4.2 * 102 N on each other. What will be the force if they are moved so they are only one-eighth as far apart?

Two small charged spheres are 6.52 cm apart. They are moved, and the force each exerts on the other is found to have tripled. How far apart are they now

A person scuffing her feet on a wool rug on a dry day accumulates a net charge of How many excess electrons does she get, and by how much does her mass increase?

(II) What is the total charge of all the electrons in a 12-kg bar of gold? What is the net charge of the bar? (Gold has 79 electrons per atom and an atomic mass of 197 u.)

Compare the electric force holding the electron in orbit around the proton nucleus of the hydrogen atom, with the gravitational force between the same electron and proton. What is the ratio of these two forces?

Particles of charge and are placed in a line (Fig. 1652). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two.

Three positive particles of equal charge, are located at the corners of an equilateral triangle of side 15.0 cm (Fig. 1653). Calculate the magnitude and direction of the net force on each particle due to the other two.

A charge Q is transferred from an initially uncharged plastic ball to an identical ball 24 cm away. The force of attraction is then 17 mN. How many electrons were transferred from one ball to the other?

A charge of 6.15 mC is placed at each corner of a square 0.100 m on a side. Determine the magnitude and direction of the force on each charge

At each corner of a square of side there are point charges of magnitude Q, 2Q, 3Q, and 4Q (Fig. 1654). Determine the magnitude and direction of the force on the charge 2Q.

A large electroscope is made with leaves that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26 angle with the vertical (Fig. 1655), what total charge Q must have been applied to the electroscope? Ignore the mass of the wires

Two small nonconducting spheres have a total charge of (a) When placed 28.0 cm apart, the force each exerts on the other is 12.0 N and is repulsive. What is the charge on each? (b) What if the force were attractive?

Two charges, and are a distance apart. These two charges are free to move but do not because there is a third (fixed) charge nearby. What must be the magnitude of the third charge and its placement in order for the first two to be in equilibrium?

(I) Determine the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2460 N/C that points due east.

A proton is released in a uniform electric field, and it experiences an electric force of toward the south. Find the magnitude and direction of the electric field

Determine the magnitude and direction of the electric field 21.7 cm directly above an isolated charge

A downward electric force of 6.4 N is exerted on a charge. Find the magnitude and direction of the electric field at the position of this charge

Determine the magnitude of the acceleration experienced by an electron in an electric field of How does the direction of the acceleration depend on the direction of the field at that point?

Determine the magnitude and direction of the electric field at a point midway between a and a charge 6.0 cm apart. Assume no other charges are nearby

Draw, approximately, the electric field lines about two point charges, and which are a distance apart

What is the electric field strength at a point in space where a proton experiences an acceleration of 2.4 million gs?

An electron is released from rest in a uniform electric field and accelerates to the north at a rate of Find the magnitude and direction of the electric field.

The electric field midway between two equal but opposite point charges is and the distance between the charges is 16.0 cm. What is the magnitude of the charge on each

Calculate the electric field at one corner of a square 1.22 m on a side if the other three corners are occupied by charges.

Calculate the electric field at the center of a square 42.5 cm on a side if one corner is occupied by a charge and the other three are occupied by charges

Determine the direction and magnitude of the electric field at the point P in Fig. 1656. The charges are separated by a distance 2a, and point P is a distance x from the midpoint between the two charges. Express your answer in terms of Q, x, a, and k

Two point charges, and are separated by a distance of 12 cm. The electric field at the point P (see Fig. 1657) is zero. How far from is P?

Determine the electric field at the origin 0 in Fig. 1658 due to the two charges at A and B.

You are given two unknown point charges, and At a point on the line joining them, one-third of the way from to the electric field is zero (Fig. 1659). What is the ratio Q1Q2?

Use Coulombs law to determine the magnitude and direction of the electric field at points A and B in Fig. 1660 due to the two positive charges shown. Are your results consistent with Fig. 1632b?

An electron (mass ) is accelerated in the uniform field between two thin parallel charged plates. The separation of the plates is 1.60 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate, Fig. 1661. (a) With what speed does it leave the hole? (b) Show that the gravitational force can be ignored.

The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in Fig. 1639. Assume that the net average charge (due to electron sharing) indicated on H and N atoms has magnitude 0.2e and on the indicated C and O atoms is 0.4e. Assume also that atoms on each molecule are separated by Estimate the net force between (a) a thymine and an adenine; and (b) a cytosine and a guanine. For each bond (red dots) consider only the three atoms in a line (two atoms on one molecule, one atom on the other). (c) Estimate the total force for a DNA molecule containing pairs of such molecules. Assume half are AT pairs and half are CG pairs

The total electric flux from a cubical box of side 28.0 cm is What charge is enclosed by the box?

In Fig. 1662, two objects, and have charges and , respectively, and a third object, is electrically neutral. (a) What is the electric flux through the surface that encloses all three objects? (b) What is the electric flux through the surface that encloses the third object only?

A cube of side 8.50 cm is placed in a uniform field with edges parallel to the field lines. (a) What is the net flux through the cube? (b) What is the flux through each of its six faces?

The electric field between two parallel square metal plates is The plates are 0.85 m on a side and are separated by 3.0 cm. What is the charge on each plate (assume equal and opposite)? Neglect edge effects

The field just outside a 3.50-cm-radius metal ball is and points toward the ball. What charge resides on the ball?

A point charge Q rests at the center of an uncharged thin spherical conducting shell. (See Fig. 1634.) What is the electric field E as a function of r (a) for r less than the inner radius of the shell, (b) inside the shell, and (c) beyond the shell? (d) How does the shell affect the field due to Q alone? How does the charge Q affect the shell?

How close must two electrons be if the magnitude of the electric force between them is equal to the weight of either at the Earths surface?

Given that the human body is mostly made of water, estimate the total amount of positive charge in a 75-kg person

A 3.0-g copper penny has a net positive charge of What fraction of its electrons has it lost?

Measurements indicate that there is an electric field surrounding the Earth. Its magnitude is about at the Earths surface and points inward toward the Earths center. What is the magnitude of the electric charge on the Earth? Is it positive or negative? [Hint: The electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at its center.

(a) The electric field near the Earths surface has magnitude of about What is the acceleration experienced by an electron near the surface of the Earth? (b) What about a proton? (c) Calculate the ratio of each acceleration to

A water droplet of radius 0.018 mm remains stationary in the air. If the downward-directed electric field of the Earth is how many excess electron charges must the water droplet have?

Estimate the net force between the CO group and the HN group shown in Fig. 1663. The C and O have charges and the H and N have charges where [Hint: Do not include the internal forces between C and O, or between H and N.]

n a simple model of the hydrogen atom, the electron revolves in a circular orbit around the proton with a speed of Determine the radius of the electrons orbit. [Hint: See Chapter 5 on circular motion.]

Two small charged spheres hang from cords of equal length as shown in Fig. 1664 and make small angles and with the vertical. (a) If and determine the ratio (b) Estimate the distance between the spheres.

A positive point charge is fixed at the origin of coordinates, and a negative point charge is fixed to the x axis at Find the location of the place(s) along the x axis where the electric field due to these two charges is zero.

Dry air will break down and generate a spark if the electric field exceeds about How much charge could be packed onto a green pea (diameter 0.75 cm) before the pea spontaneously discharges? [Hint: Eqs. 164 work outside a sphere if r is measured from its center.

Two point charges, and are located between two oppositely charged parallel plates, as shown in Fig. 1665. The two charges are separated by a distance of Assume that the electric field produced by the charged plates is uniform and equal to Calculate the net electrostatic force on Q and give its direction.

Packing material made of pieces of foamed polystyrene can easily become charged and stick to each other. Given that the density of this material is about estimate how much charge might be on a 2.0-cm-diameter foamed polystyrene sphere, assuming the electric force between two spheres stuck together is equal to the weight of one sphere.

A point charge at the end of an insulating cord of length 55 cm is observed to be in equilibrium in a uniform horizontal electric field of when the pendulums position is as shown in Fig. 1666, with the charge 12 cm above the lowest (vertical) position. If the field points to the right in Fig. 1666, determine the magnitude and sign of the point charge.

Two small, identical conducting spheres A and B are a distance R apart; each carries the same charge Q. (a) What is the force sphere B exerts on sphere A? (b) An identical sphere with zero charge, sphere C, makes contact with sphere B and is then moved very far away. What is the net force now acting on sphere A? (c) Sphere C is brought back and now makes contact with sphere A and is then moved far away. What is the force on sphere A in this third case?

For an experiment, a colleague of yours says he smeared toner particles uniformly over the surface of a sphere 1.0 m in diameter and then measured an electric field of near its surface. (a) How many toner particles (Example 166) would have to be on the surface to produce these results? (b) What is the total mass of the toner particles?

A proton is suspended at rest in a uniform electric field Take into account gravity at the Earths surface, and determine E B .

A point charge of mass 0.185 kg, and net charge hangs at rest at the end of an insulating cord above a large sheet of charge. The horizontal sheet of fixed uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the cord is measured to be 5.18 N. Calculate the magnitude and direction of the electric field due to the sheet of charge (Fig. 1667)

An electron with speed is traveling parallel to an electric field of magnitude (a) How far will the electron travel before it stops? (b) How much time will elapse before it returns to its starting point?

Given the two charges shown in Fig. 1668, at what position(s) x is the electric field zero?

What is the total charge of all the electrons in a 25-kg bar of aluminum? (Aluminum has 13 electrons per atom and an atomic mass of 27 u.)

Two point charges, and of mass m, are placed on the ends of a massless rod of length which is fixed to a table by a pin through its center. If the apparatus is then subjected to a uniform electric field E parallel to the table and perpendicular to the rod, find the net torque on the system of rod plus charges

Determine the direction and magnitude of the electric field at point P, Fig. 1669. The two charges are separated by a distance of 2a. Point P is on the perpendicular bisector of the line joining the charges, a distance x from the midpoint between them. Express your answers in terms of Q, x, a, and k.

A mole of carbon contains electrons. Two electrically neutral carbon spheres, each containing 1 mole of carbon, are separated by 15.0 cm (center to center). What fraction of electrons would have to be transferred from one sphere to the other for the electric force and the gravitational force between the spheres to be equal?