# Homework Assignment #1

Due: Tuesday 9 June 1998

Chapters 23 and 24.

### QUESTIONS

Chapter 23 - 2, 4, 7, 8, 11, 12, 15, 18, 19, 20, 22, 23, 26, 31.
Chapter 24 - 2, 4, 8, 11, 14.

### PROBLEMS

Chapter 23 - 7, 16A, 16, 18, 19, 23, 28, 39, 42, 43, 44.
Chapter 24 - 1, 5A, 5, 6, 10, 14, 24, 25, 32, 38, 43A, 43, 48, Review Problem.

These are the ANSWERS only, not the SOLUTIONS. It is not sufficient to copy these and turn them in as homework. You must show your work.

Q 23-2) Electrons are lighter and more mobile than the positive ions.

Q 23-4) Before touching, the induced charge causes attraction. After touching, the rubber rod the transfers some of its negative charge by conduction to the metal sphere; now both the rod and the sphere are negatively charged and so repel each other.
Q 23-7) The electric charges are static, not flowing in a current through your body; it is the current through your heart that interferes with its beating.
Q 23-8) The charged object (such as a rubber rod) never touches the conductor that is being charged by induction. In contrast, there must be contact between the rod and the conductor if it is charged by conduction.
Q 23-11) No, interchanging positive and negative has no effect.
Q 23-12) A large test charge might distort all of the other charges that are creating the electric field.
Q 23-15) Yes.
Q 23-18) The electrical forces have the same magnitude but opposite direction. The electron has a larger acceleration because it has a smaller mass. F=ma.
Q 23-19) The magnitude of E approaches infinity.
Q 23-20) Downward.
Q 23-22) At infinity.
Q 23-23) Midway between them.
Q 23-26) Yes.
Q 23-31) Humid air conducts electricity better than dry air. The charge "leaks off" the rubbed surfaces, which become neutral again.
Q 24-2) It is positive.
Q 24-4) No.
Q 24-8)
1. The total induced charge (that on the inner surface added to that on the outer surface) of the shell is zero.
2. On the inner surface, the point charge induces charge of the opposite sign with more found close to the point charge and less further away. On the outer surfare, charge of the same sign as the point charge is spread evenly over the surface.

Q 24-11)
1. The outer suface of the hollow conductor would never carry any charge. Erase the plus signs on the outer surface of the hollow shell in figures (b), (c), and (d). All else remains the same.
2. If the small charged ball were an insulator and the hollow conductor were NOT grounded, then the positive charge remains on the blue ball in all four figures. Figures (a) and (b) do not change; figure (c) should look like figure (b); and in figure (d) the small blue ball has positive charge while the hollow conductor has no charge on either surface.

Q 24-14) Outside, the electric fields are identical. Inside, the electric fields are different.
P 23-7) 0.873 newtons at 330 degrees (polar form).
P 23-16A) m=QE/g
P 23-16) 1.49 grams
P 23-18) Show that ...
P 23-19)
1. 1.29 x 104 N/C j (where j is a unit vector in the y direction)
2. -3.87 x 10-2 N j

P 23-23)
1. at the center of the equilateral triangle
2. Sqrt(3) k q2/a2 j

P 23-28) 1.59 x 106 N/C toward the rod
P 23-39) -2.16 x 107 N/C j (where j is a unit vector in the x direction)
P 23-42) picture required
P 23-43)
1. q1/q2 = -1/3
2. q1 is negative; q2 is positive

P 23-44) electron: 4.39 x 106 m/s; proton: 2.39 x 103 m/s
P 24-1) zero
P 24-5A) E = Phi/(pi d2/4)
P 24-5) 4.14 x 106 N/C
P 24-6) q/epsilon0
P 24-10)
1. S1: -Q/epsilon0
2. S2: 0
3. S3: -2Q/epsilon0
4. S4: 0

P 24-14) 2.26 x 105 N.m2/C
P 24-24) 1.15 x 10-9 C/m2
P 24-25)
1. 0
2. 7.2 x 106 N/C

P 24-32)
1. 1.62 x 107 N/C
2. 8.1 x 106 N/C
3. 1.62 x 106 N/C

P 24-38)
1. 2.56 x 106 N/C radially inward
2. 0

P 24-43A)
1. -q/(4 pi a2)
2. (Q+q)/(4 pi b2)

P 24-43)
1. -9.95 x 10-5 C/m2
2. +3.82 x 10-4 C/m2

P 24-48) The sphere with the large positive charge induces charge separation in the other sphere. Negative charges collect near the sphere with the large positive charge, and positive charges are pushed to the far side. The force of attraction between unlike charges nearby is greater than the force of repulsion between like sign charges far away.
P 24-Review)
1. +2Q
3. 2kQ/r2
4. zero
5. zero
6. +3Q
7. 3kQ/r2
8. 3Qr3/a3
9. 3kQr/a3
10. inner:-3Q; outer:+2Q
11. linear from r=0 to r=a;
decaying like r-2 from r=a to r=b;
zero from r=b to r=c;
and decaying like r-2 for r>c.

Please report any corrections to Professor Scalise.