Q21. Gauss’ Law

1. A particle with charge 5.0- C is placed at the corner of a

cube. The total electric flux in N m2/C through all sides

of the cube is :

1. 0

2. 7.1 104

3. 9.4 104

4. 1.4 105

5. 5.6 105

9 6

0

14 9 10 5.0 10

8insideQ

4 27.07 10 /Nm C

The corner of a cube is shared by 8 adjacent cubes.

Only 1/8 of a charge at the corner is inside the cube.

2. A round wastepaper basket with a 0.15-m radius opening is in a

uniform electric field of 300 N/C, perpendicular to the opening.

The total flux through the sides and bottom, in Nm2/C, is :

1. 0

2. 4.2

3. 21

4. 280 5. can't tell without knowing the

areas of the sides and bottom

221.2 /Nm C

2300 / 0.15N C

No flux through the sides.

3. A 3.5-cm radius hemisphere contains a total charge of

6.6 × 10–7 C. The flux through the rounded portion

of the surface is 9.8 × 104 N m2/C. The flux

through the flat base is :

1. 0

2. +2.3 × 104 N

m2/C

3. –2.3 × 104 N

m2/C

4. –4.9 × 104 N

m2/C

5. +4.9 × 104 N

m2/C

9 7 44 9 10 6.6 10 9.8 10

4 22.33 10 /Nm C

4. Two large insulating parallel plates carry charge of equal

magnitude, one positive and the other negative, that is

distributed uniformly over their inner surfaces. Rank the

points 1 through 5 according to the magnitude of the electric

field at the points, least to greatest.

1. 1, 2, 3, 4, 5

2. 5, 4, 3, 2, 1

3. 1, 4, and 5 tie, then 2 and 3 tie

4. 2 and 3 tie, then 1 and 4 tie, then

5

5. 2 and 3 tie, then 1, 4, and 5 tie

1 4 5 0E E E

2 3E E

5. Two large parallel plates carry positive charge of equal

magnitude that is distributed uniformly over their inner

surfaces. Rank the points 1 through 5 according to the

magnitude of the electric field at the points, least to greatest.

1. 1, 2, 3, 4, 5

2. 5, 4, 3, 2, 1

3. 1, 4, and 5 tie, then 2 and 3 tie

4. 2 and 3 tie, then 1 and 4 tie, then

5

5. 2 and 3 tie, then 1, 4, and 5 tie

1 4 5E E E

2 3 0E E

6. A solid insulating sphere of radius R contains a positive

charge that is distributed with a volume charge density that

does not depend on angle but does increase with distance

from the sphere center. Which of the graphs below

correctly gives the magnitude E of the electric field as a

function of the distance r from the center of the sphere :

1. A

2. B

3. C

4. D

5. E

2 3

0

1 44

3inE r c r r

2

03in

cE r

2out

QE

r

7. Which of the following graphs represents the magnitude of

the electric field as a function of the distance from the center

of a solid charged conducting sphere of radius R :

1. A

2. B

3. C

4. D

5. E

2out

QE k

r

0inE

8. Charge Q is distributed uniformly throughout an insulating

sphere of radius R. The magnitude of the electric field at a

point R/2 from the center is :

1. Q / 40

R2

2. Q / 0 R2

3. 3Q / 40

R2

4. Q / 80

R2

5. none of

these

2 3

30

1 44

42 3 23

R Q RE

R

208

QE

R