Name: Lab Day/Time: Multiple-Choice Homework 6 Gauss’ Law II Multiple-Choice Hom

Question

Name: Lab Day/Time: Multiple-Choice Homework 6 Gauss’ Law II

Multiple-Choice Homework Problem 6.1 A uniform surface charge density is spread on a spherical surface of radius a. The total charge of the system is Q. What is the electric field for radii inside the charge (r < a)?

(a) zero
(b) Q/40r2 (c) Q/40r (d) Q2/40r2 (e) Q2/40r

Multiple-Choice Homework Problem 6.2 The figure to the right shows two charged spherical shells. The inner shell has radius a and charge density a = . The outer shell has radius b and charge density b = +2. Calculate the electric field in Region II between the two shells (a < r < b).

y

Ia Air

Air Air

III
II

x b

(a) 0
(b) rˆ

40r2 (c)+ rˆ

40r2
( d ) 4 a 2 rˆ

40r2
( e ) + 4 a 2 rˆ

40r2
(f) 4a2+8b2rˆ

Problems

Select One of the Following:

Select One of the Following:

40r2

Multiple-Choice Homework Problem 6.3 Given the field map to the right, where the field in the regions labelled A and B is unknown, use Gauss’ Law to determine the sign of the charge in the regions.

(a) A is positive and B is positive. (b) A is positive and B is negative. (c) A is negative and B is positive. (d) A is negative and B is negative.

Multiple-Choice Homework Problem 6.4 A pith ball (a small sphere of tree bark) has mass m = 60mg = 6 × 105kg and receives a charge of +1nC = 1 × 109C when zapped with the electrophorous. Our electrostatic generator (the Van de Graaff) has a spherical surface with radius 12.5cm. When in operation a substantial surface charge is transferred to the sphere. If the pith ball is placed directly on top of the Van de Graaff generator (without transferring charge), how much total charge must be placed on the Van de Graaff to lift the pith ball against the force of gravity?

A

B

Select One of the Following:

1

Select One of the Following:

(a) 20nC (b) 0.6C (c) 1C (d) 5C (e) 150C

Multiple-Choice Homework Problem 6.5 An infinite plane of charge with uniform charge density 1 = occupies the y z plane through the origin. A parallel plane through x = 1cm has charge density 2 = /2. Compute the electric field in the region between the planes.

(a) 3/2o0xˆ (b) /4o0xˆ (c) 3/4o0xˆ (d) /4o0xˆ (e) -3/4o0xˆ

Multiple-Choice Homework Problem 6.6 Select the choice that follows the describes the relation between the electric force on a charged particle and the direction of the electric field lines.

(a) There is no relation between the direction of the electric force and the direction of a field line. (b) The electric force always points in the same direction as the field line.
(c) The electric force always points in the opposite direction as the field line.
(d) The electric force points either the same direction or in the opposite direction as the field line. (e) The electric force is always perpendicular to the field line.

Multiple-Choice Homework Problem 6.7 A uniform volume charge (shown in grey) occupies the region r < a and has volume charge density . The total charge of the volume charge is +2Q. A thin spherical shell of radius b > a surrounds the volume charge. The total charge of the thin spherical shell is Q. Calculate the electric field in the region (Region II) between the volume charge and the shell (a < r < b).

(a) Q rˆ 40r2

(b) 2Q rˆ 40r2

(c) 2 rˆ 40r2

(d) rˆ 40r2

( e ) r rˆ 30

Select One of the Following:

Select One of the Following:

Air
Air

volume charge

shell charge

b a

I
II

III

Select One of the Following:

2

Multiple-Choice Homework Problem 6.8 Two infinite parallel

planes of charge with uniform surface charge densities are parallel

to the x z plane and equally spaced about the origin. The

planes pass through the points ±1cm. The plane passing through

+1cmyˆ has surface charge density 3 . The plane passing through 2

1cmyˆ has surface charge density 5. The planes are drawn to the right. Compute the electric field at the origin.

(a) +13/4o0yˆ (b) 13/4o0yˆ (c) +13/2o0yˆ (d) 13/2o0yˆ (e) +7/4o0yˆ

(f) 7/4o0yˆ (g) +7/2o0yˆ (h) 7/2o0yˆ

Multiple-Choice Homework Problem 6.9 If a metal sphere of radius 1cm is charged with a “D” cell battery, a charge of 1.7 × 1012C is developed. If this sphere is then placed in a cubic box with edges of length 30.0cm. What is the electric flux out of the box?

(a) 2.7 × 1015Nm2/C (b) 4.6 × 1014Nm2/C (c) 1.7 × 104Nm2/C (d) 5.2 × 103Nm2/C (e) 0.19Nm2/C

Multiple-Choice Homework Problem 6.10 Two particles with positive charge +Q and +2Q are evenly spaced about the origin on the y axis. About what plane(s) is the system symmetric?

(a) The system is not symmetric about any plane.
(b) The system is symmetric about the x z plane.
(c) The system is symmetric about the y z plane.
(d) The system is symmetric about the xz and the yz plane.

y

+ 32

x

+5

Select One of the Following:

Select One of the Following:

y

+Q

+2Q

x

Select One of the Following:

3

Explanation / Answer

I can give only 4 ques. response at a time.

6.1) Zero, as whole charge is on the surface.(option a)

6.4) (option c) Force of the gravity on the ball = Fg = -mg (y cap)

Electric force of Van der graaf on ball= Fe = F12 = kq1q2/r12^2 (r12 cap)

In order to pith ball to hover, Fe + Fg =0

mg = kq1q2/r12^2 ===> q1 =mgr12^2/kq2 = (6*10^-5*9.8*0.125^2)/(8.99*10^9*1*10^-9) = 1 nC

6.5)   (option c)   3/4o0xˆ

6.9) (option e) Flux =q/e0 = 1.7*10^-12/8.85*10^-12 = 0.19 Nm2/C

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