1

4

32

1

Q1

Q 2

E 2

E 1

conducting sphere

conductingspherical shell

Given ,

Sketch the electric field vectors at points 2, 3 and 4

1E

e is the electric flux through the closed surfaces below, and + and - represent equal but opposite charges:

e = (no. of outgoing field lines) - (no. of ingoing field lines)

Which of the following are true?

-+-

++-

+-

++-

+ + + --

e < 0

e = 0

e > 0

e < 0

e = 0

e > 0

e < 0

e = 0

e > 0

e < 0

e = 0

e > 01. 2.

3. 4.

(a)(b)

(c)

(a)(b)

(c)

(a)(b)

(c)

(a)(b)

(c)

i

insiden i

i o

qE A

Considering the spherical “Gauss surface” through points 1, 2, 3, 4,Is Q1 : a) zero b) +ve c) –ve?

Considering the spherical “Gauss surface” through point 5,Is Q2 : a) zero b) +ve c) –ve?

Recall Gauss’ law

1

4

32

1

Q1

Q 2

E 2

E 1

conducting sphere

conductingspherical shell

5

(No calculation needed.)

i

insiden i

i o

qE A

Recall Gauss’ law

1

4

32

1

Q1

Q 2

E 2

E 1

conducting sphere

conductingspherical shell

Considering that E=0 inside the shell material, is the charge on the inside surface of the shell:

a) zero b) - Q1 c) Q2

d) - Q2 e) Q2 - Q1

Hint: Draw a Gauss surface inside the shell material.

xy

z

area AE E x

What is the electric flux Φe through the area A ?

a) E

b) EA

c) Ax

d) None of the above

xy

z

area A

E E x

What is the flux through area A ?

a) EA

b) EA sin

c) EA cos

d) none of the above

The conducting plate below carries a charge -Q. For the Gauss surface shown, which is the correct value of the electric flux through the Gauss surface?

e

A1

A2

A3

A6A5

A4Gausssurface

(d) Zero

(a) = (A1 + 2A2 + 2A3 + 2A4 + 2A5 + A6 ) x Ee

(b) = A1 x 0 + 2A2 x 0 + 2A3 x 0 + (2A4 + 2A5 + A6 ) x Ee

(c) =A1 x 0 + 2A2 x 0 + 2A3 x 0 + 2A4 x 0

+ 2A5 x 0 + A6 x E

e

Hints: (1) Draw field lines from the plate

(2) e n ii

E Ai

e

-Q

r

Gausssurface

Conductingsphere

The conducting sphere below carries a charge -Q. What is the value of the electric flux through the concentric spherical Gauss surface with radius r?

Note: F kQ Q

rk

F qE E A

e eo

e ni

ii

2

1

4 w h ere (C o u lo m b ' s law )

,

,

2 2

(a) (b)

(c) 4 (d)

(e)

e eo o

e o e

e o

Q Q

Q r Q r

Q

x

yz

r = 0.25m

E E z zN

C 1 0 6

E = 106 N/C at point P, 0.25 m from the centre of the long charged wire.

What is the charge q in a length l = 0.10 m of the wire?

2

2

2

12 2 2

(a)

(b)

(c) (2 2 )

(d) 2

8.854 10 C /Nm

o

o

o

o

o

q r E

q r lE

q r rl E

q rlE

where

Hints: - Use Gauss' law to determine Q if you know E. First,

sketch field lines. Choose Gauss surface so En = constant everywhere on it.

P

l

Field at r from spherical charge q.

Gauss' law says:

For the spherical charge below,

1. Sketch the form of the electric field lines, with an arrow to show direction.

2. Choose a Gauss surface which is where you want to calculate the electric field and its shape is such that = constant everywhere on it.

0

Total outgoing flux i

insidee n i

i

qE A

q

E

E

3. Determine the normal component of on this surface (En)

4. Divide the surface into bits of area A. What is the value of EnA on one of these bits?

5. What is the sum of all the EnA?

6. From Gauss' law, what is the value of E at the distance r from the centre of the spherical charge?

E