conducting
sphere
Q2
1
4
1

E1

E2
Q1
2
conducting
spherical shell
3
Given E1 ,
Sketch the electric field vectors at points 2, 3 and 4
Ne is the electric flux through the closed surfaces below, and + and represent equal but opposite charges:
Ne = (no. of outgoing field lines) - (no. of ingoing field lines)
Which of the following are true?
1.
+ +
-
(a) Ne > 0
(b) Ne < 0
(c) Ne = 0
+ + +
3.
(a) Ne > 0
(b) Ne < 0
(c) Ne = 0
+2.
(a) Ne > 0
(b) Ne < 0
(c) Ne = 0
+
+ +- 4.
(a) N e > 0
(b) N e < 0
(c) N e = 0
conducting
sphere
Q2
1
4
1

E1
Q1
2
conducting
spherical shell
3

E2
5
Recall Gauss’ law
qinside
 Eni Ai 
i
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?
(No calculation
needed.)
o
conducting
sphere
Q2
1
4
1

E1

E2
Q1
Recall Gauss’ law
qinside
 Eni Ai 
2
conducting
spherical shell
3
i
o
Considering that E=0 inside the shell material, is
the charge on the inside surface of the shell:
a) zero
b) - Q1
d) - Q2
e) Q2 - Q1
c) Q2
Hint: Draw a Gauss surface
inside the shell material.

E  Ex
area A
y
x
z
What is the electric flux Φe through the area A ?
a) E
b) EA
c) Ax
d) None of the above

E  Ex
area A

y
x
z
What is the flux through area A ?
a) EA
b) EA sin 2
c) EA cos 2
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  e
through the Gauss surface?
A2
A4
A1
A3
Gauss
A6 surface
A
5
Hints: (1) Draw field lines from
the plate
(2)
e 
E
ni
 Ai
i
(a)  e = (A1 + 2A2 + 2A3 + 2A4 + 2A5 + A6 ) x E
(b)  e = A1 x 0 + 2A2 x 0 + 2A3 x 0 + (2A4 + 2A5 + A6 ) x E
(c)  e =A1 x 0 + 2A2 x 0 + 2A3 x 0 + 2A4 x 0
(d) Zero
+ 2A5 x 0 + A6 x E
The conducting sphere below carries a
charge -Q. What is the value of the
electric flux  e through the
concentric spherical Gauss surface
with radius r?
-Q
r
Note: F  ke
Q Q
1
where ke 
, (Coulomb's law)
2
r
4 o


F  qE ,
e 
E
ni
 Ai
i
(a)  e  
Q
o
(c)  e  Q  4 o r 2
(e)  e  Q o
(b)  e 
Q
o
(d)  e  Q   r 2
Conducting
sphere
Gauss
surface
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?
(a) q   o r 2 E

E  Ez  106
(b) q   o r lE
2
(c) q   o (2 r 2  2 rl ) E
(d) q  2 o rlE
P
12
2
C /Nm
N
C
z
r = 0.25m
z
l
where
 o  8.854 10

y
x
2
Hints: - Use Gauss' law to determine Q if you know E.
First,
sketch field lines. Choose Gauss surface so En = constant everywhere
on it.
Field at r from spherical charge q.
Gauss' law says:
Total outgoing flux e   Eni Ai 
i
qinside
0
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 EE = constant everywhere on it.
3. Determine the normal component of E on this surface (En)
4. Divide the surface into bits of area )A. What is
the value of En)A on one of these bits?
5. What is the sum of all the En)A?
6. From Gauss' law, what is the value of E at the
distance r from the centre of the spherical charge?
q