Physics 196 Fall 2010
Exam 2
Credits for numerical questions require evidence of calculation
Name:
Some Physics Constants: electronic charge
Coulomb constant e = 1.6×10 -19
C k = 9.0×10 9
Nm
Permittivity of free space ε
0
= 8.85×10
-12
2
C
/C
2
2
/Nm
2
Mass of electron m e
= 9.11×10
-31
kg
Mass of proton m p
= 1.67×10
-27
kg
PART 1 ( 48 points total. 3 points each.)
1.
The diagram shows a uniform electric field between two parallel plates and two locations A and B between the plates. Which of the following statements regarding the electric potentials V
A
and V
B
at these points are true?
A
B
(a)
(b)
(c)
V
A

V
B
V
A

V
B
V
A

V
B
(d) No statement can be made because the points lie on different field lines
2.
A lithium nucleus
3
Li
7
and a boron nucleus
5
B
10
at rest are both accelerated by the same electric potential difference. If the final kinetic energy of the boron nucleus is K, that of the lithium nucleus is a.
5K/3 b.
3K/5 c.
7K/10 d.
10K/7
3.
The electric potential measured in volts in a region of space is given by V ( x )

9

5 x
2 where x is in meters.
The electric field in this region is a.
b.
c.

5 x ( V
15 x ( V
10 x ( V
/ m ) i
ˆ
/ m ) i
ˆ
/ m ) i
ˆ d.

10 x ( V / m ) i
ˆ
1

4.
The electric field measured in V/m in a region of space is

E
 
8 x
3 i
ˆ
where x is in meters. The potential difference V(x=2)-V(x=1) between the points at x=2 and x=1 is a.
+30V b.
–30V c.
–60V d.
+60V
5.
In a certain region where there is an electric field, its is found that the minimum work required to move a point charge of

4 nC from point A to point B is 2 .
00

J . You can conclude that a.
The point B has higher potential than A and the potential difference is 5000V b.
The point A has higher potential than B and the potential difference is 50000V c.
The point B has higher potential than A and the potential difference is 500V d.
The point A has higher potential than B and the potential difference is 500V
6.
Enumerate the errors in the following diagram showing a family of equi-potential surfaces, electric field lines (with arrows) and point charges. (solid circles represent positive charges and open circle represent negative charges)
7.
On the x-axis, a point charge of situated at the point x
 
3 m
4 .
0 nC
. Find the is situated at the origin and another point charge of x

8 .
0 nC
-coordinates of two points on the x-axis where the electric is potential vanishes. a. b. c. d. x x x x




2 .
0 m

2 .
0 m


1 .
0 m

1 .
0 m x x x x

3 .
0 m



6
3 .
0 m
6 .
.
0
0 m m
2

8.
Three point charges q ,

2 q ,

4 q are situated at three corners of a square with side a as shown. Find the electric potential at the unoccupied corner. q a
-2q
-4q a. b.

0 .
62 kq /

1 .
7 kq / a a c. d.


3 .
0 kq /
3 .
8 kq / a a
9.
Ho much work is required to establish the charge configuration of the previous problem by bringing in the point charges from infinity one at a time? a. 2 .
6
2 kq / a b. 3 .
2
3 kq / a c. 2 .
6 kq / a d. 3 .
3 kq / a
10.
An alpha particle (helium nucleus) at rest is placed at a distance 5.0×10 -10 m from a magnesium nucleus which contains 12 protons. Pushed away from the electrostatic repulsion, what is the highest kinetic energy of the alpha particle? a.
14 eV b.
57 eV c.
69 eV d.
81 eV
3

11.
The radius of the spherical dome of a van-de-Graaf generator is 3.0m. Can it be safely charged to an electric potential of 10 million volts if the breakdown electric field in air is 3MV/m? Give convincing reason . a.
Yes b.
No
12.
A solid spherical conductor of radius 1.0m has charge Q=30nC on it. It is connected to a second, initially uncharged, spherical conductor of radius 2.0m by a very long metallic wire. The electric potential of the smaller sphere is now a.
120V b.
90V c.
60V d.
30V
13.
Three identical capacitors with a capacitance of 4pF each are connected as shown. Find the equivalent capacitance. a.
3 pF b.
4 pF c.
5 pF d.
6 pF
14.
A parallel-plate capacitor is first charged up by connecting to a voltage source. The voltage source is then disconnected, and the distance between the plates is then increased. Circle the correct statement or statements in the following: a.
The capacitance increases b.
The voltage across the capacitor increases c.
The charge on the capacitor decreases d.
The electric field between the plates is unchanged
4

15.
The diagram shows a positively charged rod brought near two metallic spheres in contact with each other.
Sphere A is closer to the charged rod than B. Which of the following statements regarding the electric potentials V
A
and V
B
is necessarily correct?
A B a.
b.
c.
d.
V
A

V
B
V
A

V
B
V
V
A
B


V
0
B
16.
A 2 .
00

F capacitor is energized to a potential difference of 12 .
0 V . The wires connecting the capacitor to the battery are then disconnected from the battery and connected across a second, initially uncharged capacitor. The potential difference across the 2 .
00

F capacitor then drops to 8 .
0 V . What is the capacitance of the second capacitor? a.
4.0μF b.
3.0μF c.
2.0μF d.
1.0μF
5

PART B (52 points total)
1.
A ring of radius a carrying a uniform line charge density
 lies on the y-z plane with its center at the origin. z y x a.
( 5 points) Determine the electric potential at the point (x,0,0) on the x-axis. b.
( 3 points) Sketch the electric potential as a function of x from
 
to
  c.
( 4 points ) Determine the x
 component of the electric field at the point ( x , 0 , 0 ) d.
( 3 points) Find the x-coordinate of a point on the x-axis where the magnitude of the electric field is maximum.
6

2.
A capacitor is made up of concentric thin spherical shells of radii a and a a and a

, while that between radii 2 and a charge Q is placed on the inner shell and –Q on the outer shell. a. ( 5 points) Find the electric field at radius r separately for a
 r

2 a and 2 a
 r

3 a
2a
3a c.
( 5 points) Find the potential V
 inner
V outer
between the inner and the outer shells. d.
( 2 points) Find the capacitance.
7

3.
In a parallel-plate capacitor, the area of each plate is 500 cm
2
and the separation between the plates is
3.0mm. The space between the plates is completely occupied by a dielectric whose dielectric constant is 4. It is found that a maximum voltage of 25kV can be applied between the plates without causing dielectric breakdown. a.
( 5 points) What is the capacitance of the capacitor? b.
( 5 points) What is the stored charge and stored energy when the maximum voltage is applied? c.
( 5 points) What is the strength of the dielectric in MV/m? d.
( 5 points) How much work is required to remove the dielectric after the plates are disconnected from the voltage source?
8