Kuwait University ```Kuwait University
Physics Department
Physics 102
Second Midterm Examination
Spring Semester (201)
April 20,2013
Time: 15.30 to 17.00
Name……….………………………… Student No.……………….
Instructors: Drs. Abdelkarim, Afrousheh, Davis, Kokaj, Lajko, Marafi, Pichler,
Rakshani, Rao, Razee & Sharma
(Fundamental constants)
k=
1
 9.0 10 9 N. m 2 / C 2
4 
(Coulomb constant)
o = 8.85  10-12 C2 / (N·m2)
(Permittivity of free space)
0 = 4  10-7 T .m/A
(Premeability of free space)
e  = 1.60  10-19 C
(Elementary unit of charge)
NA = 6.02  1023
g = 9.8 m/s2
(Acceleration due to gravity)
me= 9.11  10-31 kg
(Electron mass)
mp = 1.67  10-27 kg
(Proton mass)
Prefixes of units
m = 10-3
k = 103
 = 10-6
M = 106
n = 10-9
G = 109
p = 10-12
T = 1012
For use by Instructors only
Prob.
1
2
3
4
5
6
7
8
Total
1
2
3
4
5
6
7
8
Total
Marks
Ques.
Marks
Problems
1. Calculate the equivalent capacitance between points
and . Given C = 4 μF.
C L  4F ;
[3 point]
C M  4F  4F ;
C R  4F  4F  4F
1
1 1 1 11
24
F
  

 C eq 
C eq 4 8 12 24
11
2. Initially uncharged, identical capacitors
) are connected to a circuit as
shown. The switch is at position 1 for a long time then it is switched to position 2. Find the final
potential energy stored in C1.
[5 point]
Q0  C R V 0
V 
Q0
C R V0


C eq C L  C R
4 F 24V
 16V
2 F  4 F
VC1  V  / 2  8V
U
C1V 2
 128J
2
3. The drift velocity of the electrons is vd  4.5  10 4 m/s in a copper wire of resistivity
. The density of the electrons is
electric field in the wire.
.
Find the uniform
[2 points
E  J  nqvd 
 0.105 N / C
4. In a wire the current is changing with time as I(t) = (2A/s)t. Find the number of electrons that
flow through the wire between 3 s and 6 s.
Q(t )   I (t )dt 
6
2
 (2 A / s)tdt  (t )
6
3

2
 27 C
N
27C
 1.7  10 20
19
1.6  10 C
[4 points]
5. In the circuit below I1= 3 A. Find the resistance R.
[6 points]
I 3 I 1  I 2
14V  3 A4  I 3 R  0
14V  3 A4  I 2 6  10V  0
Solution
I 2  2 A
I 3  1A
R  2
6. In the circuit shown, the switch is closed at t = 0. Find the time at which the energy of the
1
capacitor reaches one-ninth ( ) of its final value.
9
[5 points]
U ( )
 U (t ) 
9
2
1 Q fin (C ) 2


9 2C
9  2C
t / RC
]) 2
Q 2 (t ) (C[1  e



2C
2C
1
2
 [1  e t / RC ]2  e t / RC  
9
3
t  RC ln(3 / 2)  0.41

7.
A proton enters a region of uniform magnetic field B  (iˆ  2 ˆj  kˆ) T with velocity

v  (4 ˆj  kˆ) km/s. Find the magnitude of magnetic force acting on the proton when it enters the
region.

 
F  qv  B  q(6iˆ  ˆj  4kˆ)10 3 Tm / s 
[4 points]
F  q 6 2  12  4 2 10 3 Tm.s  1.2  10 15 N


8. An electron enters and leaves a region of uniform magnetic field B in the same plane ( B is per-
pendicular to this plane). If the speed of the electron is v0  3 10 3 m/s and R = 10 cm, find the
direction and magnitude of the magnetic field.
R
mv
mv
B

|q|B
|q|R
 1.7  10 7 T
inward
[3 points]
Conceptual Questions. Tick the best answer. (1 point for each question.)
1. A capacitor is charged by a battery and it is kept connected to the battery. Then a dielectric
material (K = 4) is inserted between the plates. Which statement is correct for the electric field
and the energy stored in the capacitor?
a. The electric field increases by a factor of 4, the energy decreases by a factor of 4.
b. Both the electric field and the energy remain the same.
c. The electric field decreases by a factor of 4, the energy increases by a factor of 4.
d. The electric field remains the same, the energy increases by a factor of 4.√
2. In which circuits is the final energy stored in the capacitor the highest?
a. A.
b. B.
c. C. √
d. Energies are identical.
3. The diameter of a 8 m-long copper wire linearly changes from 6 mm (point A) to 3 mm (point
B), as shown. The wire carries a current I. The electric field at point A is 100 N/C. The electric
field at point B is
a. 400 N/C.√
b. 200 N/C.
c.
50 N/C.
d.
25 N/C.
4. A potential difference V is applied to the two ends of a cylindrical wire. If the diameter of the
wire and the potential difference V are doubled, then the energy dissipation on the wire
a. decreases by a factor of 2.
b. increases by a factor of 4.
c. decreases by a factor of 8.
d. increases by a factor of 16.√
5. Three wires made of different metals have identical resistances at T0. If the temperature coefficients of the resistivities satisfy α1 < α2 < α3, then at T < T0 the resistance is smallest in wire
a. 1.
b. 2.
c. 3.√
d. There is not enough information to decide.
6. In the figure, the current I1 is 2 A.
Which current is 0.5 A?
a. I2.
b. I3.
c. I4. √
d. I5.
7. In the circuits below, the switches are initially in position 1 then at t = 0 all of them are switched
to position 2. If the time constant τ = RC = 4 s, in which circuit will the current be the largest at
8 s?
a. In circuit A. √
b. In circuit B
c. In circuit C.
d. The currents are identical.
8. Three charged particles with identical masses and velocities are entering and leaving the region
of uniform magnetic field, as shown in the figure. Which particle has the smallest charge?
a. Particle 1.
b. Particle 2.
c. Particle 3.√
d. Each has identical charge.
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