Kuwait University
Physics Department
Physics 102
Second Midterm Examination
Summer Semester 2014
June 23 2015
Time: 9.00 p.m. to 10.30 p.m.
Name……….………………………… Student No.……………….
Instructors: Drs. Abdelkarim, Farhan, Kokaj, Marafi, Sharma, Vagenas
(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
(Avogadro’s number)
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
Part I: Solve the following problems. Show your solutions in detail
1. Three capacitors, with capacitances C1 = 4.0 μF, C2 = 3.0 μF , and C3 = 2.0 μF are connected to a
12V voltage source, as shown in the figure. What is the potential difference across capacitor C2 ?
[4 points]
C23 = C2 + C3 = 5 μF
1
Ceq
1
=C +
1
𝐶1
1
C2 3
12 V
20
⟹ Ceq =
9
𝐶3
𝐶2
μF
Q = 12 Ceq = 26.7 μC
V2 = V2 3 =
Q
C2 3
= 5.3 V
2. Four capacitors, with vacuum capacitances as indicated in figure, are connected across a 90-V voltage
source. A dielectric of constant ҡ = 2 is inserted in each of the upper two capacitors filling the space
between the plates. Calculate the charge on the equivalent capacitor.
1
C2 4
=
1
1
8
3
4.0 µF
2.0 µF
3
+8=8
4
⟹ C2 4 =
[5 points]
μF
4.0 µF
1
C4 2
=
C4 2 =
Ceq =
1
4
4
3
8
1
3
2
4
+ =
2.0 µF
90 V
μF
4
+ 3 = 4 μF
3
q eq = 360 μ C
1
3. A charge Q= ˗ 610 nC is uniformly distributed on a ring of radius R = 2.4 m. A point charge
q = +480 nC is fixed at the center of the ring, as shown in the figure. An electron is projected
from infinity toward the ring along the axis of the ring. This electron momentarily stops at a
point on the axis that is 5.0 m from center of the ring. What is the initial speed of the electron
at infinity?
[4 points]
Q
VQ =
kQ
= −990
1
(R2 + x2 ) ⁄2
R
q
Vq = k
q
+
= 864 V
x
V = VQ + Vq = −126 V
2e𝑉
vi = √ m = 6.7 × 106 m⁄s
e
4. In the circuit shown in the figure, with the switch S open, the 40.0 µF capacitor has an initial
stored energy of 2 × 10-7 J while the other three capacitors are uncharged. The switch is then
closed and left closed for a long time. Calculate the final total electrical energy stored in these
four capacitors.
Ui =
[6 points]
10.0 µF
Q2
S
2C
Q2
⟹ 2 × 10−7 = 80 ×10−6
+
⟹ 𝑄 = 4 μC
˗
1
C12
=
1
10
+
40.0 µF
14.0 µF
1
15
15.0 µF
⟹ C12 = 6 μF
Ceq = 40 + 14 + 6 = 60 μF
Uf =
Q2
2Ceq
⟹ Uf =
16 × 10−12
120 ×10−6
4
= 3 × 10−7 J
2
5. A cylindrical wire of radius 2.0 mm carries a current of 2.5 A. The potential difference between
points on the wire that are 46 m apart is 3.7 V. Calculate the resistivity of the material of which
the wire is made.
𝑅=
𝑉
𝐼
[4 points]
3.7
= 2.5 = 1.48 𝛺
𝐿
𝑅 = 𝜌𝐴
⟹ 𝜌=
𝜋𝑟 2 𝑅
𝐿
= 4 × 10−7 𝛺𝑚
6. A current of 120 pA flows in a copper wire of diameter 2.0 mm. Calculate the electron drift
speed assuming the current is uniform.
n = 8.5 × 1028 per cubic meter)
J=
I
A
(The density of free electrons for copper is
[3 points]
= 38.2 × 10−6 A⁄m2
J = n q vd
J
J
vd = qn
= 2.8 × 10−15 m/s
3
7. A wire of resistance 9.0 Ω is connected to an ideal battery of voltage V = 2.0 V. Calculate how
much energy is converted from chemical to electrical form in 5 minutes.
P=
V2
R
=
U = Pt =
4
[2 points]
w
9
4
9
(5 × 60) = 133 J
8. A long thin straight wire carries a uniform linear charge density of 358 nC/m. Starting from the
formula for the electric field E, derive an expression for the potential difference between 2 points
at perpendicular distances ra, rb from the wire, (rb > ra), given that they are not near either end of
the wire. Evaluate the value of the potential difference for ra = 5.0 m & rb = 6.0 m.
E=
λ
2πϵo r
=
[4 points]
2kλ
r
r
r dr
Va − Vb = ∫r 𝑏 E dr = 2kλ ∫r 𝑏
𝑎
= 2 kλ 𝑙n
𝑎
r
r𝑏
r𝑎
Va − Vb = 1175 V
4
Part II: Objective Questions
Tick (
) the best answer in the following. Each question carries one point.
1. A negative charge is moved from point A to point B along an equipotential surface. Which
of the following statements must be true?
a) The charge performs work.
b) No work is required to move the charge.
c) The work done on the charge depends on the distance between A and B.
d) Negative work is done in moving the charge.
2. The graph in the figure shows the variation of the electric potential V(x)
V(x)
as a function of the position x. Which of the choices below correctly
describes the orientation of the x-component of the electric field along
the x-axis?
a) Ex is positive from x = ˗2 to x = 2.
b) Ex is positive from x = ˗2 to x = 0, and negative from x = 0 to x = 2.
c) Ex is negative from x = ˗2 to x = 0, and positive from x = 0 to x = 2.
d) Ex is negative from x = ˗2 to x = 2.
-2 -1.5-1 -0.5 0.5 1 1.5 2
3. If the electric potential in a region is given by V(x) = 6/x2, the x-component of the electric
field in that region is
a) ˗12 x˗3
b) ˗ 6 x
c) 12 x ˗3
d) 6 x
4. The electric field between the plates of a parallel-plate capacitor has magnitude E. The
potential across the plates is maintained at constant value by a battery as they are pulled apart
to twice their original separation. The magnitude of the electric field between the plates is now
equal to
a) 4 E
b) 2 E
c) E
d) E/2
5. A spherical capacitor has capacitance C. If both radii are doubled, what is the new
capacitance?
a) 4C
b) 2C
c) C
d) C/2
5
x
6. Two capacitors, C1 and C2, are connected in series across a source of potential difference.
With the potential source still connected, a dielectric is now inserted between the plates of
capacitor C1. What happens to the charge on capacitor C2?
a) It increases.
b) It decreases.
c) It remains the same.
d) It becomes zero.
7. A cylindrical wire has a resistance R and resistivity ρ. If its length and diameter are both cut
in half, what will be its resistivity?
a) 4 ρ
b) 2 ρ
c) ρ
d) ρ/2
8. Two wires A & B are made of the same metal have equal lengths. The resistance of wire A
is three times greater than that of wire B. What is the ratio of the cross-sectional area of A to
B?
a) 3
b) √3
c) 1
d)
1
3
6