Name__________________________

PHYSICS 112, Chapter 22-25, Test 2

Instructions:

0. General Instructions: Put your books, notes, etc. on the floor. Leave at least one seat between the nearest student. Raise your hand if you have any questions, statements or concerns. Please do not converse with your neighbors until after the exam. If your calculator has memory, erase it before beginning the exam.

1. Do your work on the test paper provided. Additional paper will be provided as needed.

2. Mark your answers with units in the spaces provided. (Always, always, check your units!) Leave the problem you have chosen to omit, blank.

3. Leave your papers open. Put your name on each paper turned in, especially the answer sheet.

Equations:

Coulomb’s Law F= k q₁q₂ / r² = 1/(4pe₀) q₁q₂ / r²

Gauss’ Law F= q/e₀ = ò E · dA

Constants:

Elementary charge, q 1.60 x 10^-19 C

Permittivity constant, e₀ 8.85 x 10^-12 F/m

Do any 3 of the following 4 problems. (16 pts each)

[1] Identical isolated conducting spheres 1 and 2 have equal amounts of charge, Q, and are separated by a distance large compared with their diameters. The electrostatic force acting on sphere 2 due to sphere 1 is F (fig. A). Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (fig. B), then to sphere 2 (fig. C) and finally removed (fig D). In terms of Q, what are the charges on spheres 1 & 2 at stages (B), (C), and (D)? In terms of F, what is the electrostatic force F’ that now acts on sphere 2?

1 2 1 2 1 2 1 2

-F F -F’ F’

(A) (B) (C) (D)

[2] An object having a mass of 2.00 g and a charge of +8.00x10^-5C is placed in an electric field E with E_x=3.00x10³ N/C, E_y=-600 N/C, and E_z=0. (a) What are the magnitude and direction of the force on the object? (b) If the object is released from rest at the origin, what will be its coordinates after 3.00 s?

[3] A solid nonconducting sphere of radius R has a nonuniform charge distribution of volume charge density r = r_sr/R, where r_s is a constant and r is the distance from the center of the sphere. (a) Show that the total charge on the sphere, Q = pr_sR³. (b) Show that the electric field inside the sphere at a point r has a magnitude given by |E| = 1/(4pe₀) Q r² / R⁴. (c) In what direction does the electric field point?

r

R

[4] In the figure below, point P is at the center of the rectangle. With V=0 at infinity, what is the net electric potential at P due to the six charged particles?

+5.0 q -2.0q -3.0q

d P d

d d

+3.0q -2.0q +5.0q

Do all of the following Multiple Choice (3pts each)

[5] A charge +Q is placed 2d away from q₁. A second charge, q₂, is placed above as shown in the figure. Rank the following arrangements according to the magnitude of the net electrostatic force (positive direction to the right) on the particle with charge +Q: (1) q₁=q₂=p (a proton); (2) q₁=e (an electron), q₂=p; (3) q₁=p, q₂=e; (4) q₁=q₂=e.

2d

+Q q₁

d

q₂

[A] 1,3,2,4 [B] 4,2,3,1 [C] 1,2,3,4 [D] 2,4,3,1 [E] 3,1,2,4

[6] Initially sphere A has a charge of -50e and sphere B has a charge of +20e. The spheres are made of conducting material and are identical in size. If the spheres then touch, what is the resulting charge on sphere A? [A] 0e [B] 10e [C] -15e [D] -30e [E] 70e

[7] The following figure 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?

+q (1) -3q -q (2) +3q +3q (3) -q -3q (4) +q

[A] 1 [B] 2 [C] 1,2 [D] 3,4 [E] 1,3

[8] The following figure shows three nonconducting rods, two circular and 2 straight. Each has uniform charge of magnitude Q along its top half, and another along its bottom half. For each rod, draw in the direction of the electric field at point P.(Clearly!)

-Q +Q +Q -Q

P P P P

+Q +Q -Q -Q

[9] The following figure shows the path of negatively charged particle 1 through a rectangular region of uniform electric field; the particle is deflected toward the top of the page. Which direction is the electric field pointed?

[A] left [B] right [C] up [D] down

[10] In the figure above, clearly draw in the trajectories of the remaining 3 particles, using the information from question 9.

[11] The figure shows three Gaussian surfaces half-submerged in a large thick metal plate with uniform surface charge density. Surface S₁ is the tallest and has the smallest square end caps; surface S₃ is the shortest and has the largest square end caps; and S₂ has intermediate values. Rank the surfaces according to the charge they enclose:

S₁ S₂ S₃

[A] 1>2>3 [B] 3>2>1 [C] 1>3>2 [D] 3>1>2 [E] 1=2=3

[12] The figure shows three situation in which a Gaussian cube sits in an electric field. The arrows and values indicate the directions and magnitudes (in N m²/C) of the flux through the six sides of each cube. (Dotted arrows are for hidden faces.) In which situations does the cube enclose positive,+ net charge, zero 0 net charge, negative - net charge?

5 3 10 3 6 8

7 3 2

4 5 5

2 4 7

7 6 5

[A] +,0,- [B] 0,+,- [C] -,+,0 [D] -,0,+ [E] 0,-,+

[13] In problem 12, rank the surfaces according to the magnitude of the electric field at the top cap.

[A] 1>2>3 [B] 3>2>1 [C] 1>3>2 [D] 3>1>2 [E] 1=2=3

[14] In problem 12, rank the surfaces according to the net electric flux through that top end cap.

[A] 1>2>3 [B] 3>2>1 [C] 1>3>2 [D] 3>1>2 [E] 1=2=3

[15] The figure shows a family of parallel equipotential surfaces in cross section, and five paths along which we shall move an electron from one surface to another. Rank the paths according to the work we do, greatest first. [Write the rank this way: 1>2>3… etc. Ties can be indicated with “=”, as in …>4=5]

1

2

3

4

5

90V 80V 70V 60V 50V 40V

[16] The figure gives the electric potential V as a function of distance through five regions on the x-axis. Rank the regions according to the magnitude of the x component of the electric field within them, greatest first.

V

1 2 3 4 5

X

[Please rank as in problem 15, ties can be indicated with “=” signs]

[17] In problem 16, clearly draw arrows indicating the direction of the field for each region. If there is no electric field, draw a circle.