What fields are especially important?

Where do electric fields come from?

What if the charge is continuous?

What fields are especially important?

What is a parallel-plate capacitor?

How do charges respond to fields?

Three equal point charges q are located on the y-axis at y = 0 and at y = {d. What is the electric field at a point on the x-axis?

At the dot, the electric field points a. Left. b. Right. c. Up. d. Down. e. The electric field is zero.

The water molecule H2O has a permanent dipole moment of magnitude 6.2 * 10-30 Cm. What is the electric field strength 1.0 nm from a water molecule at a point on the dipoles axis?

A piece of plastic is uniformly charged with surface charge density ha. The plastic is then broken into a large piece with surface charge density hb and a small piece with surface charge density hc. Rank in order, from largest to smallest, the surface charge densities ha to hc.

shows a thin, uniformly charged rod of length L with total charge Q. Find the electric field strength at radial distance r in the plane that bisects the rod.

Which of the following actions will increase the electric field strength at the position of the dot? a. Make the rod longer without changing the charge. b. Make the rod shorter without changing the charge. c. Make the rod wider without changing the charge. d. Make the rod narrower without changing the charge. e. Add charge to the rod. f. Remove charge from the rod. g. Move the dot farther from the rod. h. Move the dot closer to the rod.

A thin ring of radius R is uniformly charged with total charge Q. Find the electric field at a point on the axis of the ring (perpendicular to the ring)

Rank in order, from largest to smallest, the electric field strengths Ea to Ee at these five points near a plane of charge.

A 10-cm-diameter plastic disk is charged uniformly with an extra 1011 electrons. What is the electric field 1.0 mm above the surface at a point near the center?

Rank in order, from largest to smallest, the forces Fa to Fe a proton would experience if placed at points a to e in this parallel-plate capacitor.

Two 1.0 cm * 2.0 cm rectangular electrodes are 1.0 mm apart. What charge must be placed on each electrode to create a uniform electric field of strength 2.0 * 106 N/C? How many electrons must be moved from one electrode to the other to accomplish this?

Which electric field is responsible for the protons trajectory?

Two 6.0-cm-diameter electrodes are spaced 5.0 mm apart. They are charged by transferring 1.0 * 1011 electrons from one electrode to the other. An electron is released from rest just above the surface of the negative electrode. How long does it take the electron to cross to the positive electrode? What is its speed as it collides with the positive electrode? Assume the space between the electrodes is a vacuum

An electron gun creates a beam of electrons moving horizontally with a speed of 3.3 * 107 m/s. The electrons enter a 2.0-cm-long gap between two parallel electrodes where the electric field is E u = (5.0 * 104 N/C, down). In which direction, and by what angle, is the electron beam deflected by these electrodes?

Two 1.0 g balls are connected by a 2.0-cm-long insulating rod of negligible mass. One ball has a charge of +10 nC, the other a charge of -10 nC. The rod is held in a 1.0 * 104 N/C uniform electric field at an angle of 30 with respect to the field, then released. What is its initial angular acceleration?

The water molecule H2O has a permanent dipole moment of magnitude 6.2 * 10-30 C m. A water molecule is located 10 nm from a Na+ ion in a saltwater solution. What force does the ion exert on the water molecule?

In a vacuum chamber, a proton orbits a 1.0-cm-diameter metal ball 1.0 mm above the surface with a period of 1.0 ms. What is the charge on the ball?

Youve been assigned the task of determining the magnitude and direction of the electric field at a point in space. Give a step-bystep procedure of how you will do so. List any objects you will use, any measurements you will make, and any calculations you will need to perform. Make sure that your measurements do not disturb the charges that are creating the field

Reproduce FIGURE Q23.2 on your paper. For each part, draw a dot or dots on the figure to show any position or positions (other than infinity) where E u = 0 u .

Rank in order, from largest to smallest, the electric field strengths E1 to E4 at points 1 to 4 in FIGURE Q23.3. Explain

A small segment of wire in FIGURE Q23.4 contains 10 nC of charge. a. The segment is shrunk to one-third of its original length. What is the ratio \(\lambda_{\mathrm{f}} / \lambda_{\mathrm{i}}\), where \(\lambda_{\mathrm{i}}\) and \(\lambda_{f}\) are the initial and final linear charge densities? b. A proton is very far from the wire. What is the ratio \(F_{f} / F_{i}\) of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk? c. Suppose the original segment of wire is stretched to 10 times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?

An electron experiences a force of magnitude F when it is 1 cm from a very long, charged wire with linear charge density l. If the charge density is doubled, at what distance from the wire will a proton experience a force of the same magnitude F?

FIGURE Q23.6 shows a hollow soda straw that has been uniformly charged with positive charge. What is the electric field at the center (inside) of the straw? Explain.

The irregularly shaped area of charge in FIGURE Q23.7 has surface charge density hi . Each dimension (x and y) of the area is reduced by a factor of 3.163. a. What is the ratio hf /hi , where hf is the final surface charge density? b. An electron is very far from the area. What is the ratio Ff /Fi of the electric force on the electron after the area is reduced to the force before the area was reduced?

A circular disk has surface charge density 8 nC/cm2 . What will the surface charge density be if the radius of the disk is doubled?

A sphere of radius R has charge Q. The electric field strength at distance r 7 R is Ei . What is the ratio Ef /Ei of the final to initial electric field strengths if (a) Q is halved, (b) R is halved, and (c) r is halved (but is still 7 R)? Each part changes only one quantity; the other quantities have their initial values.

The ball in FIGURE Q23.10 is suspended from a large, uniformly charged positive plate. It swings with period T. If the ball is discharged, will the period increase, decrease, or stay the same? Explain.

Rank in order, from largest to smallest, the electric field strengths E1 to E5 at the five points in FIGURE Q23.11. Explain

A parallel-plate capacitor consists of two square plates, size L * L, separated by distance d. The plates are given charge {Q. What is the ratio Ef /Ei of the final to initial electric field strengths if (a) Q is doubled, (b) L is doubled, and (c) d is doubled? Each part changes only one quantity; the other quantities have their initial values.

A small object is released at point 3 in the center of the capacitor in FIGURE Q23.11. For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it accelerate or move at constant speed? a. A positive object is released from rest. b. A neutral but polarizable object is released from rest. c. A negative object is released from rest.

A proton and an electron are released from rest in the center of a capacitor. a. Is the force ratio Fp/Fe greater than 1, less than 1, or equal to 1? Explain. b. Is the acceleration ratio ap/ae greater than 1, less than 1, or equal to 1? Explain.

Three charges are placed at the corners of the triangle in FIGURE Q23.15. The + + charge has twice the quantity of charge of the two - charges; the net charge is zero. Is the triangle in equilibrium? If so, explain why. If not, draw the equilibrium orientation.

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.1? Specify the direction as an angle above or below horizontal

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.2? Specify the direction as an angle above or below horizontal.

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.3? Specify the direction as an angle above or below horizontal.

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.4? Specify the direction as an angle above or below horizontal

An electric dipole is formed from two charges, {q, spaced 1.0 cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point 1x, y2 = 10 cm, 10 cm2 is 360 N/C. a. What is the charge q? Give your answer in nC. b. What is the electric field strength at the point 1x, y2 = 110 cm, 0 cm2?

An electric dipole is formed from {1.0 nC charges spaced 2.0 mm apart. The dipole is at the origin, oriented along the x-axis. What is the electric field strength at the points (a) 1x, y2 = 110 cm, 0 cm2 and (b) 1x, y2 = 10 cm, 10 cm2?

An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment 1.0 * 10-7 C m is 25 cm from a small ball charged to +25 nC, with the ball on the axis of the electric dipole. What is the magnitude of the electric force on the ball?

The electric field strength 10.0 cm from a very long charged wire is 2000 N/C. What is the electric field strength 5.0 cm from the wire?

A 10-cm-long thin glass rod uniformly charged to +10 nC and a 10-cm-long thin plastic rod uniformly charged to -10 nC are placed side by side, 4.0 cm apart. What are the electric field strengths E1 to E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm from the glass rod along the line connecting the midpoints of the two rods?

Two 10-cm-long thin glass rods uniformly charged to +10 nC are placed side by side, 4.0 cm apart. What are the electric field strengths E1 to E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left along the line connecting the midpoints of the two rods?

A small glass bead charged to + 6.0 nC is in the plane that bisects a thin, uniformly charged, 10-cm-long glass rod and is 4.0 cm from the rods center. The bead is repelled from the rod with a force of 840 mN. What is the total charge on the rod?

The electric field 5.0 cm from a very long charged wire is (2000 N/C, toward the wire). What is the charge (in nC) on a 1.0-cm-long segment of the wire?

A 12-cm-long thin rod has the nonuniform charge density l1x2 = 12.0 nC/cm2e-x/16.0 cm2 , where x is measured from the center of the rod. What is the total charge on the rod? Hint: This exercise requires an integration. Think about how to handle the absolute value sign

Two 10-cm-diameter charged rings face each other, 20 cm apart. The left ring is charged to -20 nC and the right ring is charged to +20 nC. a. What is the electric field E u , both magnitude and direction, at the midpoint between the two rings? b. What is the force on a proton at the midpoint?

Two 10-cm-diameter charged rings face each other, 20 cm apart. Both rings are charged to +20 nC. What is the electric field strength at (a) the midpoint between the two rings and (b) the center of the left ring?

Two 10-cm-diameter charged disks face each other, 20 cm apart. The left disk is charged to -50 nC and the right disk is charged to +50 nC. a. What is the electric field E u , both magnitude and direction, at the midpoint between the two disks? b. What is the force F u on a -1.0 nC charge placed at the midpoint?

The electric field strength 2.0 cm from the surface of a 10-cm-diameter metal ball is 50,000 N/C. What is the charge (in nC) on the ball?

A 20 cm * 20 cm horizontal metal electrode is uniformly charged to +80 nC. What is the electric field strength 2.0 mm above the center of the electrode?

Two 2.0-cm-diameter insulating spheres have a 6.0 cm space between them. One sphere is charged to +10 nC, the other to -15 nC. What is the electric field strength at the midpoint between the two spheres?

Youve hung two very large sheets of plastic facing each other with distance d between them, as shown in FIGURE EX23.20. By rubbing them with wool and silk, youve managed to give one sheet a uniform surface charge density h1 = -h0 and the other a uniform surface charge density h2 = +3h0. What are the electric field vectors at points 1, 2, and 3?

A 2.0 m * 4.0 m flat carpet acquires a uniformly distributed charge of -10 mC after you and your friends walk across it several times. A 2.5 mg dust particle is suspended in midair just above the center of the carpet. What is the charge on the dust particle?

Two circular disks spaced 0.50 mm apart form a parallel-plate capacitor. Transferring 3.0 * 109 electrons from one disk to the other causes the electric field strength to be 2.0 * 105 N/C. What are the diameters of the disks?

A parallel-plate capacitor is formed from two 6.0-cm-diameter electrodes spaced 2.0 mm apart. The electric field strength inside the capacitor is 1.0 * 106 N/C. What is the charge (in nC) on each electrode?

Air breaks down when the electric field strength reaches 3.0 * 106 N/C, causing a spark. A parallel-plate capacitor is made from two 4.0 cm * 4.0 cm electrodes. How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

Two parallel plates 1.0 cm apart are equally and oppositely charged. An electron is released from rest at the surface of the negative plate and simultaneously a proton is released from rest at the surface of the positive plate. How far from the negative plate is the point at which the electron and proton pass each other?

Two 2.0-cm-diameter disks face each other, 1.0 mm apart. They are charged to {10 nC.a. What is the electric field strength between the disks? b. A proton is shot from the negative disk toward the positive disk. What launch speed must the proton have to just barely reach the positive disk?

Honeybees acquire a charge while flying due to friction with the air. A 100 mg bee with a charge of +23 pC experiences an electric force in the earths electric field, which is typically 100 N/C, directed downward. a. What is the ratio of the electric force on the bee to the bees weight? b. What electric field strength and direction would allow the bee to hang suspended in the air?

An electron traveling parallel to a uniform electric field increases its speed from 2.0 * 107 m/s to 4.0 * 107 m/s over a distance of 1.2 cm. What is the electric field strength?

The surface charge density on an infinite charged plane is -2.0 * 10-6 C/m2 . A proton is shot straight away from the plane at 2.0 * 106 m/s. How far does the proton travel before reaching its turning point?

An electron in a vacuum chamber is fired with a speed of 8300 km/s toward a large, uniformly charged plate 75 cm away. The electron reaches a closest distance of 15 cm before being repelled. What is the plates surface charge density?

A 1.0-mm-diameter oil droplet (density 900 kg/m3 ) is negatively charged with the addition of 25 extra electrons. It is released from rest 2.0 mm from a very wide plane of positive charge, after which it accelerates toward the plane and collides with a speed of 3.5 m/s. What is the surface charge density of the plane?

The permanent electric dipole moment of the water molecule 1H2O2 is 6.2 * 10-30 C m. What is the maximum possible torque on a water molecule in a 5.0 * 108 N/C electric field?

A point charge Q is distance r from a dipole consisting of charges {q separated by distance s. The dipole is initially oriented so that Q is in the plane bisecting the dipole. Immediately after the dipole is released, what are (a) the magnitude of the force and (b) the magnitude of the torque on the dipole? You can assume r W s.

An ammonia molecule (NH3) has a permanent electric dipole moment 5.0 * 10-30 C m. A proton is 2.0 nm from the molecule in the plane that bisects the dipole. What is the electric force of the molecule on the proton?

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.35? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive x-axis.

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.36? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive x-axis

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.37? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive x-axis.

FIGURE P23.38 shows three charges at the corners of a square. Write the electric field at point P in component form.

Charges -q and +2q in FIGURE P23.39 are located at x = {a. Determine the electric field at points 1 to 4. Write each field in component form.

Derive Equation 23.11 for the field E u dipole in the plane that bisects an electric dipole.

FIGURE P23.41 is a cross section of two infinite lines of charge that extend out of the page. Both have linear charge density l. Find an expression for the electric field strength E at height y above the midpoint between the lines.

FIGURE P23.42 is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are {l. Find an expression for the electric field strength E at height y above the midpoint between the lines.

FIGURE P23.43 shows a thin rod of length L with total charge Q. a. Find an expression for the electric field strength at point P on the axis of the rod at distance r from the center. b. Verify that your expression has the expected behavior if r W L. c. Evaluate E at r = 3.0 cm if L = 5.0 cm and Q = 3.0 nC.

FIGURE P23.44 shows a thin rod of length L with total charge Q. Find an expression for the electric field E u at point P. Give your answer in component form.

Show that the on-axis electric field of a ring of charge has the expected behavior when z V R and when z W R.

A ring of radius R has total charge Q. a. At what distance along the z-axis is the electric field strength a maximum? b. What is the electric field strength at this point?

Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into the semicircle shown in FIGURE P23.47. a. Find an expression for the electric field E u at the center of the semicircle. Hint: A small piece of arc length s spans a small angle u = s/R, where R is the radius. b. Evaluate the field strength if L = 10 cm and Q = 30 nC.

A plastic rod with linear charge density l is bent into the quarter circle shown in FIGURE P23.48. We want to find the electric field at the origin. a. Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle u. b. Write, but do not evaluate, definite integrals for the x- and y-components of the net electric field at the origin. c. Evaluate the integrals and write E u net in component form

An infinite plane of charge with surface charge density 3.2 mC/m2 has a 20-cm-diameter circular hole cut out of it. What is the electric field strength directly over the center of the hole at a distance of 12 cm? Hint: Can you create this charge distribution as a superposition of charge distributions for which you know the electric field?

A sphere of radius R and surface charge density h is positioned with its center distance 2R from an infinite plane with surface charge density h. At what distance from the plane, along a line toward the center of the sphere, is the electric field zero?

A parallel-plate capacitor has 2.0 cm * 2.0 cm electrodes with surface charge densities {1.0 * 10-6 C/m2 . A proton traveling parallel to the electrodes at 1.0 * 106 m/s enters the center of the gap between them. By what distance has the proton been deflected sideways when it reaches the far edge of the capacitor? Assume the field is uniform inside the capacitor and zero outside the capacitor.

An electron is launched at a 45 angle and a speed of 5.0 * 106 m/s from the positive plate of the parallel-plate capacitor shown in FIGURE P23.52. The electron lands 4.0 cm away. a. What is the electric field strength inside the capacitor? b. What is the smallest possible spacing between the plates?

The two parallel plates in FIGURE P23.53 are 2.0 cm apart and the electric field strength between them is 1.0 * 104 N/C. An electron is launched at a 45 angle from the positive plate. What is the maximum initial speed v0 the electron can have without hitting the negative plate?

A problem of practical interest is to make a beam of electrons turn a 90 corner. This can be done with the parallel-plate capacitor shown in FIGURE P23.54. An electron with kinetic energy 3.0 * 10-17 J enters through a small hole in the bottom plate of the capacitor. a. Should the bottom plate be charged positive or negative relative to the top plate if you want the electron to turn to the right? Explain. b. What strength electric field is needed if the electron is to emerge from an exit hole 1.0 cm away from the entrance hole, traveling at right angles to its original direction? Hint: The difficulty of this problem depends on how you choose your coordinate system. c. What minimum separation dmin must the capacitor plates have?

A positron is an elementary particle identical to an electron except that its charge is +e. An electron and a positron can rotate about their center of mass as if they were a dumbbell connected by a massless rod. What is the orbital frequency for an electron and a positron 1.0 nm apart?

Your physics assignment is to figure out a way to use electricity to launch a small 6.0-cm-long plastic drink stirrer. You decide that youll charge the little plastic rod by rubbing it with fur, then hold it near a long, charged wire, as shown in FIGURE P23.56. When you let go, the electric force of the wire on the plastic rod will shoot it away. Suppose you can uniformly charge the plastic stirrer to 10 nC and that the linear charge density of the long wire is 1.0 * 10-7 C/m. What is the net electric force on the plastic stirrer if the end closest to the wire is 2.0 cm away? Hint: The stirrer cannot be modeled as a point charge; an integration is required

The combustion of fossil fuels produces micron-sized particles of soot, one of the major components of air pollution. The terminal speeds of these particles are extremely small, so they remain suspended in air for very long periods of time. Furthermore, very small particles almost always acquire small amounts of charge from cosmic rays and various atmospheric effects, so their motion is influenced not only by gravity but also by the earths weak electric field. Consider a small spherical particle of radius r, density r, and charge q. A small sphere moving with speed v experiences a drag force Fdrag = 6phrv, where h is the viscosity of the air. (This differs from the drag force you learned in Chapter 6 because there we considered macroscopic rather than microscopic objects.) a. A particle falling at its terminal speed vterm is in equilibrium with no net force. Write Newtons first law for this particle falling in the presence of a downward electric field of strength E, then solve to find an expression for vterm. b. Soot is primarily carbon, and carbon in the form of graphite has a density of 2200 kg/m3 . In the absence of an electric field, what is the terminal speed in mm/s of a 1.0-mm-diameter graphite particle? The viscosity of air at 20C is 1.8 * 10-5 kg/m s. c. The earths electric field is typically (150 N/C, downward). In this field, what is the terminal speed in mm/s of a 1.0- mm-diameter graphite particle that has acquired 250 extra electrons?

A 2.0-mm-diameter glass sphere has a charge of +1.0 nC. What speed does an electron need to orbit the sphere 1.0 mm above the surface?

In a classical model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius 0.053 nm. What is the orbital frequency? The proton is so much more massive than the electron that you can assume the proton is at rest

An electric field can induce an electric dipole in a neutral atom or molecule by pushing the positive and negative charges in opposite directions. The dipole moment of an induced dipole is directly proportional to the electric field. That is, p u = aE u , where a is called the polarizability of the molecule. A bigger field stretches the molecule farther and causes a larger dipole moment. a. What are the units of a? b. An ion with charge q is distance r from a molecule with polarizability a. Find an expression for the force F u ion on dipole.

Show that an infinite line of charge with linear charge density l exerts an attractive force on an electric dipole with magnitude F = 2lp/4pP0r2 . Assume that r, the distance from the line, is much larger than the charge separation in the dipole.

The ozone molecule O3 has a permanent dipole moment of 1.8 * 10-30 C m. Although the molecule is very slightly bent which is why it has a dipole momentit can be modeled as a uniform rod of length 2.5 * 10-10 m with the dipole moment perpendicular to the axis of the rod. Suppose an ozone molecule is in a 5000 N/C uniform electric field. In equilibrium, the dipole moment is aligned with the electric field. But if the molecule is rotated by a small angle and released, it will oscillate back and forth in simple harmonic motion. What is the frequency f of oscillation?

In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of these a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.19.0 * 109 Nm2 /C2 2 12.0 * 10-9 C2 s 10.025 m23 = 1150 N/C

In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of these a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.19.0 * 109 Nm2 /C2 2 212.0 * 10-7 C/m2 r = 25,000 N/C

In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of these a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.2P0 c 1 - z 2z 2 + R2 d = 1 2 h 2P

In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of these a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.2.0 * 1012 m/s2 = 11.60 * 10-19 C2E 11.67 * 10-27 kg2 E = Q 18.85 * 10-12 C2 /Nm2 210.020 m22

A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density l = a 0 y 0 , where a is a constant with the units C/m2 . a. Draw a graph of l versus y over the length of the rod. b. Determine the constant a in terms of L and the rods total charge Q. c. Find the electric field strength of the rod at distance x on the x-axis

a. An infinitely long sheet of charge of width L lies in the xyplane between x = -L /2 and x = L /2. The surface charge density is h. Derive an expression for the electric field E u at height z above the centerline of the sheet. b. Verify that your expression has the expected behavior if z V L and if z W L. c. Draw a graph of field strength E versus z

a. An infinitely long sheet of charge of width L lies in the xyplane between x = -L /2 and x = L /2. The surface charge density is h. Derive an expression for the electric field E u along the x-axis for points outside the sheet 1x 7 L /22. b. Verify that your expression has the expected behavior if x W L. Hint: ln11 + u2 u if u V 1. c. Draw a graph of field strength E versus x for x 7 L /2

A thin cylindrical shell of radius R and length L, like a soda straw, is uniformly charged with surface charge density h. What is the electric field strength at the center of one end of the cylinder?

One type of ink-jet printer, called an electrostatic ink-jet printer, forms the letters by using deflecting electrodes to steer charged ink drops up and down vertically as the ink jet sweeps horizontally across the page. The ink jet forms 30@mm@diameter drops of ink, charges them by spraying 800,000 electrons on the surface, and shoots them toward the page at a speed of 20 m/s. Along the way, the drops pass through two horizontal, parallel electrodes that are 6.0 mm long, 4.0 mm wide, and spaced 1.0 mm apart. The distance from the center of the electrodes to the paper is 2.0 cm. To form the tallest letters, which have a height of 6.0 mm, the drops need to be deflected upward (or downward) by 3.0 mm. What electric field strength is needed between the electrodes to achieve this deflection? Ink, which consists of dye particles suspended in alcohol, has a density of 800 kg/m3 .

A proton orbits a long charged wire, making 1.0 * 106 revolutions per second. The radius of the orbit is 1.0 cm. What is the wires linear charge density?

You have a summer intern position with a company that designs and builds nanomachines. An engineer with the company is designing a microscopic oscillator to help keep time, and youve been assigned to help him analyze the design. He wants to place a negative charge at the center of a very small, positively charged metal ring. His claim is that the negative charge will undergo simple harmonic motion at a frequency determined by the amount of charge on the ring. a. Consider a negative charge near the center of a positively charged ring centered on the z-axis. Show that there is a restoring force on the charge if it moves along the z-axis but stays close to the center of the ring. That is, show theres a force that tries to keep the charge at z = 0. b. Show that for small oscillations, with amplitude V R, a particle of mass m with charge -q undergoes simple harmonic motion with frequency f = 1 2p B qQ 4pP0mR3 R and Q are the radius and charge of the ring. c. Evaluate the oscillation frequency for an electron at the center of a 2.0@mm@diameter ring charged to 1.0 * 10-13 C.