The magnitude of the electrostatic force between two identical ions that are separated

Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated as particles and are fixed with a certain separation. For what value of q/Q will the electrostatic force between the two spheres be maximized?

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Fig. 21-22a). The electrostatic force acting on sphere 2 due to sphere 1 is . Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Fig. 21-22b), then to sphere 2 (Fig. 21-22c), and finally removed (Fig. 21-22d). The electrostatic force that now acts on sphere 2 has magnitude F .What is the ratio F /F? (b ) 1 2 3 (c ) 1 2 (d) 1 2 3 F F' Figure 21-22 Problem 2.

What must be the distance between point charge q1  static force between A and B at the end of experiment 2 to that at the end of experiment 1? 9 Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108 N when their center-to-center separation is 50.0 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0360 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? 10 In Fig. 21-25, four particles form a square.The charges are SSM WWW 26.0 mC and point charge q2  47.0 mC for the electrostatic force between them to have a magnitude of 5.70 N?

In the return stroke of a typical lightning bolt, a current of 2.5  104 A exists for 20 ms. How much charge is transferred in this event?

A particle of charge 3.00  10 6 C is 12.0 cm distant from a second particle of charge 1.50  10 6 C. Calculate the magnitude of the electrostatic force between the particles.

Two equally charged particles are held 3.2  103 m apart and then released from rest. The initial acceleration of the first particle is observed to be 7.0 m/s2 and that of the second to be 9.0 m/s2 . If the mass of the first particle is 6.3  107 kg, what are (a) the mass of the second particle and (b) the magnitude of the charge of each particle?

In Fig. 21-23, three charged particles lie on an x axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If L23  L12, what is the ratio q1/q2? L12 L23 1 2 3 x Figure 21-23 Problems 7 and 40.

In Fig. 21-24, three identical conducting spheres initially have the following charges: sphere A, 4Q; sphere B, 6Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to-center separation that is much larger than the spheres. Two experiments are conducted. In experiment 1, sphere C is touched to sphere A and then (separately) to sphere B, and then it is removed. In experiment 2, starting with the same initial states, the procedure is reversed: Sphere C is touched to sphere B and then (separately) to sphere A, and then it is removed. What is the ratio of the electroI static force between A and B at the end of experiment 2 to that at the end of experiment 1? C A d B Figure 21-24 Problems 8 and 65.

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108 N when their center-to-center separation is 50.0 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0360 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other?

In Fig. 21-25, four particles form a square.The charges are q1  q4  Q and q2  q3  q. (a) What is Q/q if the net electrostatic force on particles 1 and 4 is zero? (b) Is there any value of q that makes the net electrostatic force on each of the four particles zero? Explain. 4 1 2 a a a a x y Figure 21-25 Problems 10, 11, and 70.

In Fig. 21-25, the particles have charges q1  q2  100 nC 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? 3 4 1 2 a a a a x y Figure 21-25 Problems 10, 11, and 70.

Two particles are fixed on an x axis. Particle 1 of charge 40 mC 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 mC 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. 21-26, particle 1 of x y 1 2 L Figure 21-26 Problems 13, 19, 30, 58, and 67. charge 1.0 mC and particle 2 of charge 3.0 mC 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 must be the (a) x and (b) y coordinates of particle 3?

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

The charges and coordinates of two charged particles held fixed in an xy plane are q1  3.0 mC, x1  3.5 cm, y1  0.50 cm, and q2  4.0 mC, x2  2.0 cm, y2  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 mC be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero?

In Fig. 21-27a, 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  1019 C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force on it. Figure 21-27b 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 q1 and (b) the ratio q2 /q1? F (1023 N) 1 0 1 0 xs x x (cm) y

In Fig. 21-28a, particles 1 and 2 have charge 20.0 mC 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. 21-28b, particle 3 of charge 20.0 mC 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? 1 2 d d 3 Figure 21-28 Problem 17.

In Fig. 21-29a, three positively charged particles are fixed on an x axis. Particles B and C are so close to each other that they can be considered to be at the same distance from particle A. The net force on particle A due to particles B and C is 2.014  10 23 N in the negative direction of the x axis. In Fig. 21- 29b, 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  10 24 N in the negative direction of the x axis. What is the ratio qC/qB? A B C A B C x x (a) (b) Figure 21-29 Problem 18.

In Fig. 21-26, 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 q3 /q?

Figure 21-30a 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 u relative to the positive direction of the x axis (Fig. 21-30b). The curves in Fig. 21-30c give, for two situations, the magnitude Fnet of the net electrostatic force on particle A due to the other particles.That net force is given as a function of angle u and as a multiple of a basic amount F0. For example on curve 1, at u  180, we see that Fnet  2F0. (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? net 2 1 0 0 90 180 1 2 (a) (b) (c) x x A C B A C Figure 21-30 Problem 20.

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 r is the charge per unit volume, with the unit coulomb per cubic meter. For this shell r  b/r, where ris the distance in meters from the center of the shell and b  3.0 mC/m2 .What is the net charge in the shell?

Figure 21-31 shows an 2 of charge q1  q2  3.20  1019 C are on a y axis at distance d  17.0 cm from the origin. Particle 3 of charge q3  6.40  1019 C is moved gradually along the x axis from x  0 to x  5.0 m. At what values of x will the magnitude of the electrostatic force on the third particle from the other two particles be (a) minimum and (b) maximum? What are the (c) minimum and (d) maximum magnitudes? Module 21-2 Charge Is Quantized 24 Two tiny, spherical water drops, with identical charges of 1.00  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? 25 ILW How many electrons would have to be removed from a Figure 21-28 Problem 17. d (a) (b ) 1 2 d d 3 A B C A B C x x (a) (b) Figure 21-29 Problem 18. 27 SSM The magnitude of the electrostatic force between two idenFnet 2 1 0 0 90 180 1 2 (a) (b) (c) x x A C B A C B d d d Figure 21-30 Problem 20. arrangement of four charged particles, with angle u 30.0 and distance d 2.00 cm. Particle 2 has charge q2 8.00  10 19 C; particles 3 and 4 have charges q3 q4 1.60  10 19 C. (a) What is distance D between the origin and 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)? 23 In x y 1 2 d D 3 4 Figure 21-31 Problem 22.

In Fig. 21-32, particles 1 and 2 of charge q1  q2  3.20  1019 C are on a y axis at distance d  17.0 cm from the origin. Particle 3 of charge q3  6.40  1019 C is moved gradually along the x axis from x  0 to x  5.0 m. At what values of x will the magnitude of the electrostatic force on the third particle from the other two particles be (a) minimum and (b) maximum? What are the (c) minimum and (d) maximum magnitudes? 1 3 d d 2 y Figure 21-32 Problem 23.

Two tiny, spherical water drops, with identical charges of 1.00  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  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  10 10 m?

The magnitude of the electrostatic force between two identical ions that are separated by a distance of 5.0  1010 m is 3.7  109 N. (a) What is the charge of each ion? (b) How many electrons are missingfrom 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. 21-33, particles 2 and 4, of charge e, are fixed in place on a y axis, at y2 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 x1 10.0 cm and particle 3 is at x3 10.0 cm. (a) To what x value must particle 1 be moved to rotate the direction of the net electric force 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 back to its original direction? y 1 3 4 2 Figure 21-33 Problem 29.

In Fig.21-26,particles 1 and 2 are fixed in place on an x axis,at a separation of L 8.00 cm.Their charges are q1 e and q2 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 on it. (a) At what coordinate should particle 3 be placed to minimize the magnitude of that force? (b) What is that minimum magnitude? 3

Earths 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 Earths 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 21-34a shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of |q1| 8.00e. Particle 3 of charge q3 8.00e is initially on the x axis near particle 2. Then particle 3 is gradually moved in the positive direction of the x axis. As a result, the magnitude of the net electrostatic force on particle 2 due to particles 1 and 3 changes. Figure 21-34b gives the x component of that net force as a function of the position x of particle 3. The scale of the x axis is set by xs 0.80 m. The plot has an asymptote of F2,net 1.5  10 25 N as x : . As a multiple of e and including the sign, what is the charge q2 of particle 2? F 2 1 0 1 0 x (m) F2, net (1025 N) xs x y 1 Figure 21-34 Problem 32.

Calculate the number of coulombs of positive charge in 250 cm3 of (neutral) water. (Hint: A hydrogen atom contains one proton; an oxygen atom contains eight protons.)

Figure 21-35 shows electrons 1 and 2 on an x axis and charged ions 3 and 4 of identical charge q and at identical angles u. Electron 2 is free to move; the other three particles are fixed in place at horizontal distances R from electron 2 and are intended to hold electron 2 in place. For physically possible values of q  5e, what are the (a) smallest, (b) second smallest, and (c) third smallest values of u for which electron 2 is held in place. Figure 21-35 Problem 34. R R x y q q e e 2 3 4 1

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 cubes center (Fig. 21-36). The edge length of the cube is 0.40 nm. SSM 34 Figure 21-35 shows electrons 1 and 2 on an x axis and charged ions 3 and 4 of identical charge q and at identical angles u. Electron 2 is free to move; the other three particles are fixed in place at horizontal distances R from electron 2 and are intended to hold electron 2 in place. For physically possible valThe 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 Cl ion by the seven remaining Cs ions? 0.40 nm + Cl Figure 21-36 Problem 35.

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) SSM 1 H  9 Be : X  n; (b) 12C  1 H : X; (c) 15N  1 H : 4 He  X. Appendix F will help.

Figure 21-37 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? A W B C Figure 21-37 Problem 38.

In Fig. 21-38, 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 d2 6.00 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1? d2 d1 1 2 Figure 21-38 Problem 39.

In Fig. 21-23, 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 L23 2.00L12, what is the ratio q1/q2? 4

(a) What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? (b) Why dont 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. 21-39, two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L.Assume that u is so small that tan u can be replaced by its approximate equal, sin u. (a) Show that x  q2 L 2p0mg  1/3 W, gives the equilibrium separation x of the balls. (b) If L 120 cm, m 10 g, and x 5.0 cm, what is |q|? L L q q x Figure 21-39 Problems 42 and 43.

(a) Explain what happens to the balls of Problem 42 if one of them is discharged (loses its charge q to, say, the ground). (b) Find the new equilibrium separation x, using the given values of L and m and the computed value of |q|.

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 Earths surface?

How many megacoulombs of positive charge are in 1.00 mol of neutral molecular-hydrogen gas (H2)?

In Fig. 21-40, four particles are fixed along an x axis, separated by distances d 2.00 cm. The charges are q1 2e, q2 e, q3 e, and q4 4e, with e 1.60  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? d dd 3 4 x Figure 21-40 Problem 46.

Point charges of 6.0 mC and 4.0 mC are placed on an SSM x  q2 L 2p0mg  1/3 What value should h have so that the rod exerts no vertical force on the bearing when the rod is horizontal and balanced? 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? 48

In Fig. 21-41, 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 B are connected by a thin wire and then disconnected; 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 B and C? A B C Figure 21-41 Problem 48.

A neutron consists of one up quark of charge 2e/3 and two down quarks each having charge e/3. If we assume that the down quarks are 2.6  1015 m apart inside the neutron, what is the magnitude of the electrostatic force between them?

Figure 21-42 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? q +Q Rod h L x

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 r is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if r is (a) uniform, with a value of 4.00 mC/m3 , and (b) nonuniform, with a value given by r bx2 , where b 2.00 mC/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 mC) 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.) 53

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 mC 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 mC. (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 cats 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  1022 copper atoms. (Hint: A neutral copper atom contains 29 protons and 29 electrons.) What do you conclude?

In Fig. 21-26, particle 1 of charge 80.0 mC and particle 2 of charge 40.0 mC 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 mC, if particle 3 is placed at (a) x 40.0 cm and (b) x 80.0 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? 59

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

In Fig. 21-43, six charged particles surround particle 7 at radial distances of either d 1.0 cm or 2d, as drawn. The charges are q1 2e,q2 4e,q3 e,q4 4e,q5 2e,q6 8e,q7 6e, with e 1.60  1019C. What is the magnitude of the net electrostatic force on particle 7? y 2 5 1 7 3 4 6 Figure 21-43 Problem 60.

Three charged particles form a triangle: particle 1 with charge Q1 80.0 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 18.0 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) 80.0 nC and (b) 80.0 nC? 6

In Fig. 21-44, 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 q1 3.20  10 19 C, q2 3.20  10 19 C, q3 6.40  10 19 C, q4 3.20  10 19 C, u1 35.0,d1 3.00 cm, and d2 d3 2.00 cm. SSM x Figure 21-44 Problem 62. d1 d2 1 d3 x y

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 mC is released from rest at x 28 cm. If the initial acceleration of the particle has a magnitude of 100 km/s2 , what is the particles mass? 6

Two small, positively charged spheres have a combined charge of 5.0  10 5 C. 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. 21-24 are the following: sphere A, Q; sphere B, Q/4; and sphere C, Q/2, where Q 2.00  10 14 C. 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? 6

An electron is in a vacuum near Earths 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? 6

In Fig. 21-26, particle 1 of charge 5.00q 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 4 He. (These are nuclei, not atoms, and thus electrons are not involved.) When the separation between 234Th and 4 He is 9.0  1015 m, what are the magnitudes of (a) the electrostatic force between them and (b) the acceleration of the 4 He particle?

In Fig. 21-25, four particles form a square. The charges are q1 Q, q2 q3 q, and q4 2.00Q. What is q/Q if the net electrostatic force on particle 1 is zero? 71

In a spherical metal shell of radius R, an electron is shot from the center directly toward a tiny hole in the shell, through which it escapes. The shell is negatively charged with a surface charge density (charge per unit area) of 6.90  1013 C/m2 . What is the magnitude of the electrons acceleration when it reaches radial distances (a) r 0.500R and (b) 2.00R?

An electron is projected with an initial speed vi 3.2  105 m/s directly toward a very distant proton that is at rest. Because the proton mass is large relative to the electron mass, assume that the proton remains at rest. By calculating the work done on the electron by the electrostatic force, determine the distance between the two particles when the electron instantaneously has speed 2vi .

In an early model of the hydrogen atom (the Bohr model), the electron orbits the proton in uniformly circular motion. The radius of the circle is restricted (quantized) to certain values given by r n2 a0, for n 1, 2, 3, . . . , where a0 52.92 pm.What is the speed of the electron if it orbits in (a) the smallest allowed orbit and (b) the second smallest orbit? (c) If the electron moves to larger orbits, does its speed increase, decrease, or stay the same? 74

A 100 W lamp has a steady current of 0.83 A in its filament. How long is required for 1 mol of electrons to pass through the lamp?

The charges of an electron and a positron are e and e. The mass of each is 9.11  1031 kg. What is the ratio of the electrical force to the gravitational force between an electron and a positron?