Solved: In Fig. 21-28a, three positively charged particles

Figure 21-12 shows four situations in which five charged particles are evenly spaced along an axis. The charge values are indicated except for the central particle, which has the same charge in all four situations. Rank the situations according to the magnitude of the net electrostatic force on the central particle, greatest first.

Figure 21-13 shows three pairs of identical spheres that are to be touched together and then separated. The initial charges on them are indicated. Rank the pairs according to (a) the magnitude of the charge transferred during touching and (b) the charge left on the positively charged sphere, greatest first.

Figure 21-14 shows four situations in which charged particles are fixed in place on an axis. In which situations is there a point to the left of the particles where an electron will be in equilibrium?

Figure 21-15 shows two charged particles on an axis. The charges are -3q -q free to move. However, a third Fig.21-15 Question 4. charged particle can be placed at a certain point such that all three particles are then in equilibrium. (a) Is that point to the left of the first two particles, to their right, or between them? (b) Should the third particle be positively or negatively charged? (c) Is the equilibrium stable or unstable?

In Fig. 21-16, a central particle of charge -q is surrounded by two circular rings of charged particles. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consider symmetry.)

A positively charged ball is brought close to an electrically neu+4q tral isolated conductor. The conduc- -2q -2q tor is then grounded while the ball is kept close. Is the conductor +4q charged positively, charged nega- Fig.21-16 Question 5. tively, or neutral if (a) the ball is first taken away and then the ground connection is removed and (b) the ground connection is first removed and then the ball is taken away?

Figure 21-17 shows three situations involving a charged particle and a uniformly charged spherical shell. The charges are given, and the radii of the shells are indicated. Rank the situations according to the magnitude of the force on the particle due to the presence of the shell, greatest first.

Figure 21-18 shows four arrangements of charged particles. Rank the arrangements according to the magnitude of the net electrostatic force on the particle with charge +Q, greatest first.

Figure 21-19 shows four situations in which particles of charge +q or -q are fixed in place. In each situation, the particles on the x axis are equidistant from the y axis. First, consider the middle particle in situation 1; the middle particle experiences an electrostatic force from each of the other two particles. (a) Are the magnitudes F of those forces the same or different? (b) Is the magnitude of the net force on the middle particle equal to, greater than, or less than 2F? (c) Do the x components of the two forces add or cancel? (d) Do their y components add or cancel? (e) Is the direction of the net force on the middle particle that of the canceling components or the adding components? (f) What is the direction of that net force? Now consider the remaining situations: What is the direction of the net force on the middle particle in (g) situation 2, (h) situation 3, and (i) situation 4? (In each situation, consider the symmetry of the charge distribution and determine the canceling components and the adding components.)

In Fig. 21-20, a central particle of charge - 2q is surrounded by a square array of charged particles, separated by either distance d or d/2 along the perimeter of the square. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consideration of symmetry can greatly reduce the amount of work required here.)

In Fig. 21-24, the particles have charges qJ = -q2 = 100nC and q3 = -q4 = 200 nC, and distance a = 5.0 cm. What are the (a) x and (b) Y components of the net electrostatic force on particle 3?

Two particles are fixed on an x axis. Particle 1 of charge 40 fLC is located at x = -2.0 cm; particle 2 of charge Q is located at x = 3.0 cm. Particle 3 of charge magnitude 20 fLC is released from rest on the y axis at y = 2.0 cm. What is the value of Q if the initial acceleration of particle 3 is in the positive direction of (a) the x axis and (b) the y axis?

In Fig. 21-25, particle 1 of charge + 1.0 fLC and particle 2 of charge -3.0 fLC are held at separation L = 10.0 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what )' _____ 1 ...... 1---........,; ......... - x r-- L -1 must be the (a) x and (b) y coordinates Fig.21-25 Problems of particle 3?

Three particles are fixed on an x axis. Particle 1 of charge q1 is atx = -a, and particle 2 of charge q2 is atx = +a. If their net electrostatic force on particle 3 of charge +Q is to be zero, what must be the ratio q11q2 when particle 3 is at (a) x = +0.500a and (b) x = + 1.50a?

The charges and coordinates of two charged particles held fixed in an xy plane are q1 = +3.0 /-LC, Xl = 3.5 cm, Y1 = 0.50 cm, and q2 = -4.0/-LC, X2 = -2.0 cm, Yz = 1.5 cm. Find the (a) magnitude and (b) direction of the electrostatic force on particle 2 due to particle 1. At what (c) x and (d) Y coordinates should a third particle of charge q3 = +4.0 /-LC be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero?

In Fig. 21-26a, particle 1 (of charge q1) and particle 2 (of charge q2) are fixed in place on an x axis, 8.00 cm apart. Particle 3 (of charge q3 = +8.00 X 10-19 C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force F;,uel on it. Figure 21-26b gives the x component of that force versus the coordinate x at which particle 3 is placed. The scale of the x axis is set by Xs = 8.0 cm.What are (a) the sign of charge ql and (b) the ratio q21q1?

In Fig. 21-27a, particles 1 and 2 have charge 20.0 /-LC each and are held at separation distance d = 1.50 m. (a) What is the magnitude of the electrostatic force on particle 1 due to particle 2? In Fig. 21-27b, particle 3 of charge 20.0 /-LC is positioned so as to complete an equilateral triangle. (b) What is the magnitude of the net electrostatic force on particle 1 due to particles 2 and 3?

In Fig. 21-28a, three positively charged particles are fixed on an x axis. Particles Band C are so close to lilT ,,~ d~ d 3" 2,,1 d/ ,,~ (a) (b) Fig. 21-27 Problem 17. ------@@__--... ~~@--x A Be (a) each other that they can be consid- ... "..-----,,@__--_,,--x ered to be at the same distance from B A e particle A. The net force on particle (b) A due to particles Band Cis 2.014 X 10-23 N in the negative direction of Fig.21-28 Problem 18. the x axis. In Fig. 21-28b, particle B has been moved to the opposite side of A but is still at the same distance from it. The net force on A is now 2.877 X 10 -24 N in the negative direction of the x axis. What is the ratio qClqB?

In Fig. 21-25, particle 1 of charge +q and particle 2 of charge +4.00q are held at separation L = 9.00 cm on an x axis. If particle 3 of charge q3 is to be located such that the three particles remain in place when released, what must be the (a) x and (b) Y coordinates of particle 3, and (c) the ratio q3lq?

Figure 21-29a shows an arrangement of three charged particles separated by distance d. Particles A and C are fixed on the x axis, but particle B can be moved along a circle centered on particle A. During the movement, a radial line between A and B makes an angle () relative to the positive direction of the x axis (Fig. 21-29b). The curves in Fig. 21-29c give, for two situations, the magnitude Fuel of the net electrostatic force on particle A due to the other particles. That net force is given as a function of angle () and as a multiple of a basic amount Fo. For example on curve 1, at () = 1800 , we see that Fnet = 2Fo. (a) For the situation corresponding to curve 1, what is the ratio of the charge of particle C to that of particle B (including sign)? (b) For the situation corresponding to curve 2, what is that ratio?

A nonconducting spherical shell, with an inner radius of 4.0 cm and an outer radius of 6.0 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density p is the charge per unit volume, with the unit coulomb per cubic meter. For this shell p = blr, where r is the distance in meters from the center of the shell and b = 3.0 /-LC/m2. What is the net charge in the shell?

Figure 21-30 shows an arrangement of four charged particles, with angle () = 30.00 and distance d = 2.00 cm. Particle 2 has charge q2 = +8.00 X 10-19 C; particles 3 and 4 have charges q3 = q4 = -1.60 X 10-19 C. (a) What is ...- ...- ...- () y 3 2 distance D between the origin and Fig.21-30 Problem 22. particle 2 if the net electrostatic force on particle 1 due to the other particles is zero? (b) If particles 3 and 4 were moved closer to the x axis but maintained their symmetry about that axis, would the required value of D be greater than, less than, or the same as in part (a)?

In Fig. 21-31, particles 1 and 2 of y charge ql = q2 = +3.20 X 10-19 Care 1 on a y axis at distance d = 17.0 cm T from the origin. Particle 3 of charge d q3 = +6.40 X 10-19 C is moved gradu- + f-------i 3 ---X ally along the x axis from x = 0 to x = d +5.0 m. At what values of x will the .L 2 magnitude of the electrostatic force on the third particle from the other two Fig. 21-31 Problem 23. particles be (a) minimum and (b) maximum? What are the (c) minimum and (d) maximum magnitudes?

Two tiny, spherical water drops, with identical charges of -1.00 X 10 -16 C, have a center-to-center separation of 1.00 cm. (a) What is the magnitude of the electrostatic force acting between them? (b) How many excess electrons are on each drop, giving it its charge imbalance?

How many electrons would have to be removed from a coin to leave it with a charge of + 1.0 X 10 -7 C?

What is the magnitude of the electrostatic force between a singly charged sodium ion (Na+, of charge +e) and an adjacent singly charged chlorine ion (Cl-, of charge -e) in a salt crystal if their separation is 2.82 X 10-10 m?

The magnitude of the electrostatic force between two identical ions that are separated by a distance of 5.0 X 10-10 m is 3.7 X 1O-9N. (a) What is the charge of each ion? (b) How many electrons are "missing" from each ion (thus giving the ion its charge imbalance)?

A current of 0.300 A through your chest can send your heart into fibrillation, ruining the normal rhythm of heartbeat and disrupting the flow of blood (and thus oxygen) to your brain. If that current persists for 2.00 min, how many conduction electrons pass through your chest?

In Fig. 21-32, particles 2 and 4, of charge -e, are fixed in place on a y axis, at yz = -10.0 cm and Y4 = 5.00 cm. Particles 1 and 3, of charge -e, can be moved along the x axis. Particle 5, of charge +e, is fixed at the origin. Initially particle 1 is at Xl = -10.0 cm and particle 3 is y 4 -.------~----~~-x 3 2 at X3 = 10.0 cm. (a) To what X value Fig.21-32 Problem 29. must particle 1 be moved to rotate the direction of the net electric force Fnet on particle 5 by 30 counterclockwise? (b) With particle 1 fixed at its new position, to what X value must you move particle 3 to rotate Fnet back to its original direction?

In Fig. 21-25, particles 1 and 2 are fixed in place on anx axis, at a separation of L = 8.00 cm. Their charges are ql = +e and qz = -27e. Particle 3 with charge q3 = +4e is to be placed on the line between particles 1 and 2, so that they produce a net electrostatic force F3 net on it. (a) At what coordinate should particle 3 be placed to minimize the magnitude ofthat force? (b) What is that minimum magnitude?

Earth's atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth's surface would intercept protons at the average rate of 1500 protons per second. What would be the electric current intercepted by the total surface area of the planet?

Figure 21-33a shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of iqli = 8.ODe. Particle 3 of charge q3 = +8.ODe is initially on the x axis near particle 2. Then particle 3 is gradually moved in the positive direction of

Can't copy problem

Can't copy problem

In crystals of the salt cesium chloride, cesium ions Cs+ form the eight corners of a cube and a chlorine ion Cl- is at the cube's center (Fig. 21-35). The edge length of the cube is 0040 nm. The Cs+ ions are each deficient by one electron (and thus each has a charge of +e), and the Cl- ion has one excess electron (and thus has a charge of - e). (a) What is the magnitude of the net electrostatic force exerted on the Cl- ion by the eight Cs+ ions at the corners of the cube? (b) If one of the Cs+ ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on the CI- ion by the seven remaining Cs+ ions?

Electrons and positrons are produced by the nuclear transformations of protons and neutrons known as beta decay. (a) If a proton transforms into a neutron, is an electron or a positron produced? (b) If a neutron transforms into a proton, is an electron or a positron produced

Identify X in the following nuclear reactions: (a) IH + 9Be -'> X + n; (b) 12C + IH -'> X; (c) 15N + IH -'> 4He + X. Appendix F will help.

Figure 21-36 shows four identical conducting spheres that are actually well separated from one another. Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of -32e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of +48e), and then they are separated. The final charge on sphere W is + 18e. What was the initial charge on sphere A?

In Fig. 21-37, particle 1 of charge +4e is above a floor by distance d1 = 2.00 mm and particle 2 of charge +6e is on the floor, at distance dz = 6.00 mm horizontally from particle 1. What is the x component of the electrostatic force on y ~-,.,T,l--f ~t~l ~...",;hc-' ~_ x ~d2~ particle 2 due to particle I?

In Fig. 21-22, particles 1 and 2 are fixed in place, but particle 3 is free to move. If the net electrostatic force on particle 3 due to particles 1 and 2 is zero and L Z3 = 2.00L1Z, what is the ratio q/qz?

a) What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? (b) Why don't you need to know the lunar distance to solve this problem? (c) How many kilograms of hydrogen ions (that is, protons) would be needed to provide the positive charge calculated in (a)?

In Fig. 21-38, two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L. Assume that (J is so small that tan (J can be replaced by its approximate equal, sin (J. (a) Show that ( qZL )113 x = 21T1>omg gives the equilibrium separation x of the balls. (b) If L = 120 cm, m = 10 g, and x = 5.0 cm, what is Iql?

(a) Explain what happens to the balls of Problem 42 if one of them is discharged (loses its charge q to, say, the Fig. 21-38 Problems 42 and 43. q ground). (b) Find the new equilibrium separation x, using the given values of Land 111 and the computed value of Iql.

How far apart must two protons be if the magnitude of the electrostatic force acting on either one due to the other is equal to the magnitude of the gravitational force on a proton at Earth's surface?

How many megacoulombs of positive charge are in 1.00 mol of neutral molecular-hydrogen gas (Hz)?

In Fig. 21-39, four particles are fixed along an x axis, separated by distances d = 2.00 cm. The charges are qj = +2e, qz = -e, q3 = +e, and q4 = +4e, with e = 1.60 X 10-19 C. In unit-vector notation, what is the net electrostatic force on (a) particle 1 and (b) particle 2 due to the other particles?

Point charges of +6.0 fLC and -4.0 fLC are placed on an x axis, at x = 8.0 m and x = 16 m, respectively. What charge must be placed at x = 24 m so that any charge placed at the origin would experience no electrostatic force?

In Fig. 21-40, three identical conducting spheres form an equilateral triangle of side length d = 20.0 cm. The sphere radii are much smaller than d, and the sphere charges are qA = -2.00 nC, qB = -4.00 nC, and qc = +8.00 nC. (a) What is the magnitude of the electrostatic force between spheres A and C? The following steps are then taken: A and Bare connected by a thin wire and then disconFig. 21-40 Problem 48. nected; B is grounded by the wire, and the wire is then removed; B and C are connected by the wire and then disconnected. What now are the magnitudes of the electrostatic force (b) between spheres A and C and (c) between spheres Band C?

A neutron consists of one "up" quark of charge +2e13 and two "down" quarks each having charge -e/3. If we assume that the down quarks are 2.6 X 10-15 m apart inside the neutron, what is the magnitude of the electrostatic force between them?

Figure 21-41 shows a long, nonconducting, massless rod of length L, pivoted at its center and balanced with a block of weight W at a distance x from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. A distance h directly beneath each of these spheres is a fixed sphere with positive charge Q. (a) Find the distance x when the rod is horizontal and balanced. (b) What value should h have so that the rod exerts no vertical force on the bearing when the rod is horizontal and balanced?

A charged nonconducting rod, with a length of 2.00 m and a cross-sectional area of 4.00 cm2, lies along the positive side of an x axis with one end at the origin. The volume charge density p is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if p is (a) uniform, with a value of -4.00 fLC/m\ and (b) nonuniform, with a value given by p = bxz, where b = -2.00 fLC/m5?

A particle of charge Q is fixed at the origin of an xy coordinate system. At t = 0 a particle (m 0.800 g, q = 4.00 fLC) is located on the x axis at x = 20.0 cm, moving with a speed of 50.0 m/s in the positive y direction. For what value of Q will the moving particle execute circular motion? (Neglect the gravitational force on the particle.)

What would be the magnitude of the electrostatic force between two 1.00 C point charges separated by a distance of (a) 1.00 m and (b) 1.00 km if such point charges existed (they do not) and this configuration could be set up?

A charge of 6.0 fLC is to be split into two parts that are then separated by 3.0 mm. What is the maximum possible magnitude of the electrostatic force between those two parts?

Of the charge Q on a tiny sphere, a fraction a is to be transferred to a second, nearby sphere. The spheres can be treated as particles. (a) What value of a maximizes the magnitude F of the electrostatic force between the two spheres? What are the (b) smaller and (c) larger values of a that put F at half the maximum magnitude?

If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair and the cotton can leave you with an excess charge of -2.00 f.J.,e. (a) How many electrons are transferred between you and the cat? You will gradually discharge via the floor, but if instead of waiting, you immediately reach toward a faucet, a painful spark can suddenly appear as your fingers near the faucet. (b) In that spark, do electrons flow from you to the faucet or vice versa? (c) Just before the spark appears, do you induce positive or negative charge in the faucet? (d) If, instead, the cat reaches a paw toward the faucet, which way do electrons flow in the resulting spark? (e) If you stroke a cat with a bare hand on a dry day, you should take care not to bring your fingers near the cat's nose or you will hurt it with a spark. Considering that cat hair is an insulator, explain how the spark can appear.

We know that the negative charge on the electron and the positive charge on the proton are equal. Suppose, however, that these magnitudes differ from each other by 0.00010%. With what force would two copper coins, placed 1.0 m apart, repel each other? Assume that each coin contains 3 X 10 22 copper atoms. (Hint: A neutral copper atom contains 29 protons and 29 electrons.) What do you conclude?

In Fig. 21-25, particle 1 of charge -SO.O f.J.,C and particle 2 of charge +40.0 f.J.,C are held at separation L = 20.0 cm on an x axis. In unit-vector notation, what is the net electrostatic force on particle 3, of charge q3 = 20.0 f.J.,C, if particle 3 is placed at (a) x = 40.0 cm and (b) x = SO.O cm? What should be the (c) x and (d) Y coordinates of particle 3 if the net electrostatic force on it due to particles 1 and 2 is zero?

What is the total charge in coulombs of 75.0 kg of electrons?

In Fig. 21-42, six charged particles surround particle 7 at radial distances of either d = 1.0 cm or 2d, as drawn. The charges are ql = +2e, q2 = +4e, q3 = +e, q4 = +4e, q5 = +2e, q6 = +Se, q7 = +6e, with e = 1.60 X 10-19 e. What is the magnitude of the net electrostatic force on particle 7?

Three charged particles form a triangle: particle 1 with charge QI = So.o nC is at xy coordinates (0, 3.00 mm), particle 2 with charge Q2 is at (0, -3.00 mm), and particle 3 with charge q = lS.0 nC is at (4.00 mm, 0). In unit-vector notation, what is the electrostatic force on particle 3 due to the other two particles if Q2 is equal to (a) SO.O nC and (b) -SO.O nC?

In Fig. 21-43, what are the (a) magnitude and (b) direction of the net electrostatic force on particle 4 due to the other three particles? All four particles are fixed in the xy plane, and ql = -3.20 X 10-19 C, q2 = +3.20 X 10-19 C, q3 = +6.40 X 10-19 C, q4 = +3.20 X 10-19 C, 81 = 35.0D ,d1 = 3.00 cm,and d2 = d3 = 2.00 cm.

Two point charges of 30 nC and -40 nC are held fixed on an x axis, at the origin and at x = 72 cm, respectively. A particle with a charge of 42 f.J.,C is released from rest at x = 2S cm. If the initial acceleration of the particle has a magnitude of 100 km/s2, what is the particle's mass?

Two small, positively charged spheres have a combined charge of 5.0 X 10 -5 e. If each sphere is repelled from the other by an electrostatic force of 1.0 N when the spheres are 2.0 m apart, what is the charge on the sphere with the smaller charge?

The initial charges on the three identical metal spheres in Fig. 21-23 are the following: sphere A, Q; sphere B, -QI4; and sphere C, Q/2, where Q = 2.00 X 10-14 e. Spheres A and B are fixed in place, with a center-to-center separation of d = 1.20 m, which is much larger than the spheres. Sphere C is touched first to sphere A and then to sphere B and is then removed. What then is the magnitude of the electrostatic force between spheres A and B?

An electron is in a vacuum near Earth's surface and located at y = 0 on a vertical y axis. At what value of y should a second electron be placed such that its electrostatic force on the first electron balances the gravitational force on the first electron?

In Fig. 21-25, particle 1 of charge -S.OOq and particle 2 of charge + 2.00q are held at separation L on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3?

Two engineering students, John with a mass of 90 kg and Mary with a mass of 45 kg, are 30 m apart. Suppose each has a 0.01 % imbalance in the amount of positive and negative charge, one student being positive and the other negative. Find the order of magnitude of the electrostatic force of attraction between them by replacing each student with a sphere of water having the same mass as the student.

In the radioactive decay of Eq. 21-13, a 238U nucleus transforms to 234Th and an ejected 4He. (These are nuclei, not atoms, and thus electrons are not involved.) When the separation between 234Th and 4He is 9.0 X 10-15 m, what are the magnitudes of (a) the electrostatic force between them and (b) the acceleration of the 4He particle?

In Fig. 21-24, four particles form a square. The charges are q1 +Q, q2 = q3 = q, and q4 = -2.00Q. What is qlQ if the net electrostatic force on particle 1 is zero?