Physics 196 Spring 2013
Exam 2
Time Allowed: 2 hours
Some Physics Constants:
Name:
e = 1.6×10-19 C
k = 9.0×109 Nm2/C2
ε0 = 8.85×10-12 C2/Nm2
me = 9.11×10-31 kg
mp = 1.67×10-27 kg
electronic charge
Coulomb constant
Permittivity of free space
Mass of electron
Mass of proton
PART A (48 points total. 4 points each.)
1. A circular disk of radius 25cm is placed in a uniform electric field of
300N / C inclined an angle of 40 with the plane of the disk. With the
direction of the normal to the disk chosen as shown, the electric flux through
the disk is
(a)
(b)
(c)
(d)
-45.1 N × m2 / C
+45.1 N × m2 / C
-37.9 N × m2 / C
+37.9 N × m2 / C
2. In the following diagram showing four point charges, draw closed surfaces through which the electric flux is
zero
1
3. In a region where there is a uniform electric field, the minimum work required to move a point charge of
3.0mC from point A to point B is 750 J . It can be concluded that
(a)
(b)
(c)
(d)
The electric potential difference between A and B is
The electric potential difference between A and B is
The electric potential difference between A and B is
The electric potential difference between A and B is
250kV with B at a higher potential
250kV with A at a higher potential
500kV with B at a higher potential
500kV with A at a higher potential
4. On the x-y plane, the electric field is uniform and is given by E = 400 ĵ(N / C)( in the y-direction). The
point A has coordinates ( 2,-1) and the point B has coordinates (-1,3) where coordinates are measured in
meters. The potential difference VB -VA is
(a)
(b)
(c)
(d)
-1, 600 V
-1, 200V
+1, 600 V
+1, 200V
5. In a rectangular coordinate system (x, y, z) in space where coordinates are measured in meters, the electric
field is given by E = -6x 2iˆ ( N C ) . Find the electric potential difference V -V between the plane A at
B
A
x =1 and the plane B at x = 5.
(a)
(b)
(c)
(d)
254 V
252 V
250 V
248 V
6. Which of the following diagrams give the correct direction of the electric field relative to the equipotential
surfaces?
(a)
(b)
(c)
2
(d)
7. On the x-y plane, the electric potential in volt is given by the function V ( x, y) = -4x 2 y2 + 5x 4 of the
coordinates x, y in meters. Determine the components of the electric field in V/m at the point (-1, 2) are
(a) Ex =12, Ey = -16
(b) Ex = -12, Ey =16
(c) Ex = -12, Ey = -16
(d) Ex =12, Ey =16
8. A bare nucleus produces an electric potential of 43.3V at a distance of 4.0 ´10-10 m away. How many
protons are there in the nucleus?
(a)
(b)
(c)
(d)
6
12
16
20
9. Radioactive decay of a certain unstable nucleus produces alpha particles (the bare nucleus of 2 He 4 ) with
kinetic energy of 4.5MeV . What is the speed of the alpha particles?
(a)
(b)
(c)
(d)
4.4 ´10 7 m / s
3.3´10 7 m / s
2.2 ´10 7 m / s
1.1´10 7 m / s
3
10. Given that air becomes conducting when the electric field exceeds 2.5´106 N / C , what is the maximum
electrical potential for a metal sphere of radius 2.0cm in air ?
(a)
(b)
(c)
(d)
50 kV
40 kV
25kV
12.5kV
11. Which of the following procedure(s) will increase the capacitance of a parallel plate capacitor?
(a)
(b)
(c)
(d)
increase its charge
increase its potential difference
reduce the distance between the plates
reduce the area of the plates
12. Find the equivalent capacitance of the following combination of identical
capacitors, each having a capacitance of C .
(a)
(b)
(c)
(d)
C/6
11C / 6
3C 2
6C / 5
4
PART B (52 points total)
13. (16 points) A parallel plate capacitors consists of two square plates of dimensions 50cm ´ 50cm separated
by a distance of 1.2cm . The plates are connected to a voltage source of 6, 000 V .
(a) (4 points) Determine the capacitance
(b) (4 points) Determine the charge, the energy stored, and the electric field between the plates
(c) (4 points) After the power supply is disconnected from the capacitor, the plates are moved apart so their
separation becomes 3.6cm . Find how much work is requited to do this.
(d) (4 points) After the step in (c), the plates are connected to an uncharged parallel plate capacitor identical
to the one in (a) ( 50cm ´ 50cm plates, separated by 1.2cm ). Find the potential difference between the
plates of the original capacitor.
5
14. (20 points) Three point charges exist on the x-axis on
the x-y plane as shown. They consist of a point charge
-2q at the origin, two point charges +3q at the points
(±a, 0) .
(a) ( 4 points) How much work is required to assemble
this configuration? (Express your answers in terms
of k, q, a )
(b) ( 4 points) Determine the electric potential at the point ( 0, a) on the y-axis.
(c) (4 points) Determine the electric potential at the point ( a, a)
6
(d) (4 points) Determine the y-coordinate of the points on the y-axis where the electric potential vanishes.
(e) (4 points) Sketch the function V ( x, 0) , the electric potential on the x-axis.
15. (16 points) A solid sphere of radius a carrying total charge q
uniformly distributed throughout its volume is surrounded by a
concentric conducting spherical shell of inner radius b and outer
radius c , carrying total charge 3q .
(a) (6 points) Determine the electric field at a distance r from the
center, separately for the cases r > c, c > r > b, b > r > a
7
(b) (4 points) Determine the electric field for r < a
By integrating the electric field, and assuming the electric potential to be zero at infinity, find the
electric potential
(c) (2 points) of the shell
(d) (2 points) at the surface of the sphere
(e) (2 points) at the center of the sphere
8
Extra Credit Problem for Exam 1 (4 points to be credited to exam 1)
2m occupies the portion of x-axis from x = -1.0m to +1.0m . It carries electric charge so that the linear
2
charge density is given by the function l ( x ) = Ax , where A is a constant. Find the electric field at the point x = 2.0m in
terms of the total charge q and the Coulomb constant k .
A thin rod of length
9