Kuwait University
Physics Department
Physics 102
Final Exam
Summer Semester (2008-2009)
August 16, 2009 (5:00- 7:00 p.m.)
Name: …………………………
Student No: ………………..
Instructors: Drs. Abel Karim, Afrousheh, Davis, Marafi,
Ramadan, Razee, Manaa, Kota Rao
(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
 = 10-6
M = 106
m = 10-3
k = 103
n = 10-9
G = 109
p = 10-12
T = 1012
For use by Instructors only
Problem
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
9
10
Total
Marks
Question
Marks
1
9
10
Total
Part I: Solve the following problems
1. Point charges q1 = +5.0 nC and q2 = ─7.0 nC below are a distance d = 0.50 m apart. The magnitude of
the electric field of q1 at point A is 370 N/C. Find the magnitude of the electric field of q2 at A. 3 points
E q1 
E q2 
kq 1
kq 1
 r1 
 0.35 m
1
E q1
r2
k q2
2
2
r

63
0.85 m2
x
A
q1
q2
d
  87 N / C
2. Two infinite uniform lines of charge in the xy-plane cross at the origin (see below); 1   2.0 nC / m ,
 2   1.5 nC / m . Find the x-component Ex of the net electric field at point P with coordinates x = 0 m,
y = 2.0 m.
3 points
(0, 2) P
 2k  2
E x  E 2 x   
 r2

 cos 


  45  , r2  2 m  E x 14 N / C
45°
2
3. The axis of a very long conducting cylinder (of radius R = 0.30 m) is on the y-axis (see figure). The
cylinder has surface charge density   4.0 C / m 2 . Calculate the magnitude of the potential difference
between the point A (at x = 0 m) and B (at x = 4.0 m) shown in the figure.
E2r  L  Q encl 0 , Q encl  2R  L
4.0 m
VA VB 

0.30 m

5 points
y
 R  1

E  

 0 r
R   4.0 
5
Edr  ln 
 3.510 V /m
 0  0.30 
0.30 m
A
B
x

4. A metal plate (of thickness a = 1.0 cm) is inserted between the plates of an air-filled parallel-plate
capacitor as shown below. The original plate separation is d = 2.5 cm; all plates have area A = 0.20 m2.
Calculate the final capacitance.
C  0
2 points
A
1.2 10 10 F
da
d
3
a
5. In the capacitor network below, the potential difference between points a and b is 12.0 V. Find the total
energy stored in this network.
4 points
6.20 µF 11.8 µF
8.60 µF
a
b
4.80 µF
3.50 µF
Calculation of Ceq
(Equivalent capacitance)
6.20 µF and 11.8 µF in series
→
Cs = 4.06 µF
Cs and 3.50 µF in parallel
→
Cp = 7.56 µF
8.60 µF, 4.80 µF and Cp in series
→
Ceq = 2.19 µF
1
U  C eq Vab2 1.58 10  4 J
2
6. In the aluminum slab below, the current density at points on cross-sectional surface S is 3.0 A/m2. What
is the current through the planar surface bounded by circle B?
3 points
 
I B  I A  J A Area of S   J A a 2  6.8 10 6 A
0.85 mm = a
1.5 V
0.65 mm = b
4
s
Circle A (radius a)
Circle B (radius b)
7. In the circuit below, the point a is grounded (Va = 0) and the potential at point b is Vb = 2.0 V.
Find the resistance R. (Define any currents you use in the circuit diagram.)
5 points
R
b  2.0 V
Vb   3.0  I R R V

 I R R 1.0 V Eq. a 
b
3.0 V
0.5A
I R  0.50 A  I 8.0 Eq. b 
4.0 V
.b 
.a 
b  2.0 V
Vb   8.0I 8.0  4 V

 I 8.0   0.25 A Eq

 I R  0.25 A Eq

 R  4.0 
a
8.0 Ω
8. The wire triangle below carries current I = 2.5 in a uniform magnetic field of magnitude B = 1.5 T. Find
the magnitude and direction of the magnetic force on side RQ of the triangle.
3 points
FB  IRQ Bsin 


Q

B
0.60 m
RQ1.0m, sin  0.8  FB 3.0N
I
I
I
r
FB perpendicularly out of page
P
0.80 m

9. The very long parallel cylindrical wires 1 and 2 (shown end-on in the figure below) carry currents
5
R
I1 = 1.0 A and I2 = 2.5 A, respectively; R = 0.020 m. Find the magnitude and direction of the net
magnetic field at point a.
5 points
Wire 1
B2 
0 I2 1
2 2.5 R
Wire 2
I1 (into)
I2 (out)
R/2
a
R
R
R
 R
 2  B1   0 I encl ,
2

I ecnl 
I1
2
 R 2 
2
R

B1 
 0 I1
22R 
B  B1  B 2 1.5 10 5 T

B perpendicularly down (in the plane of the page)

10. A single circular current loop has magnetic field Bc at its center when the current in the loop is Ic. A

long ideal solenoid (of radius R = 1.0 cm, length L = 0.4 m and N = 500 turns) has magnetic field B s at
its center when the current in the solenoid is Is. What is the radius of the loop if Bc = 0.1 Bs
when Ic = 5Is?
3 points
0Ic 1
25
L
c  5 Is
  0 nI s I
 a 
 25  2 10 2 m
2a 10
n
N
6
Part II: Conceptual questions. Tick the best answer.
1. In the following figure, the electric field at a point P between the two positive electric charges Q1 and Q2
is zero. Which statement below is most accurate? (Assume the potential is zero at infinity.)
a) Electric potential at point P is non-zero
b) Electric potential at point P is positive
Q1
c) Electric potential at point P is negative
P
Q2
d) Electric potential at point P is zero
2. An insulating rod is bent into the shape of a semi-circle as shown in the figure. The left half has a
negative charge –Q distributed uniformly along its length and the right half has a positive charge +Q
distributed uniformly along its length. Which vector shows the correct direction of the net electric field
at the center of the circle?
a) A
–
b) B
–
– –
+ +
–
A
c) C
+
+
+
D
C
d) D
B
3. A and B are parallel-plate capacitors and C and D are spherical capacitors. The equipotential surfaces
are shown by dashed lines. The correct figures are:
a) A and D
b) B and D
c) A and C
d) B and C
A
B
D
C
4. A capacitor has vacuum in the space between its plates. If you increase the plate charge by a factor of 2,
what happens to the capacitance?
a) It increases by a factor of two
b) It decreases by a factor of two
c) It remains the same
d) The answer depends on the size and shape of the conductor
5. Three point charges are placed in the xy-plane as shown in the figure. The net electric flux
through a spherical surface of radius R = 2a centered at the origin is:
a)  E  q1  q 2  q 3  /  0
q2
y
b)  E  q1  q 2  /  0
2a
c)  E  q1 /  0
2a
d)  E  0
a
q3
7
a
q1
x
6. The figures below show cross-sectional areas of four resistors of the same material and length
(perpendicular to the page). The resistances are such that:
2a
3a
a) RB < RC < RD < RA
a
3a
A
B
b) RA = RB < RC = RD
c) RB < RA < RC < RD
a
3a
2a
a
2a
d) RA = RB = RC = RD
D
C
7. All resistors and capacitors in the circuits below are identical.
The time constants are such that:
a)
τA
>
τB
>
τC
>
τD
b)
τA
=
τC
>
τB
>
τD
c)
τA
=
τC
>
τB
=
τD
d)
τA
=
τC
=
τB
=
τD
D
C
B
A


8. A negative charge moves with velocity v in a magnetic field B . Which diagram below could be

correct? ( FB is the magnetic force.)
a) (1)
b) (2)
c) (3)
d) (4)

B

v
x

FB
x

B

FB
(1)

v
(2)

v

B
.

FB

FB

v
.

B
(4)
(3)
9. Below, two very long straight wires (carrying equal currents i) cross each other perpendicularly.
In which quadrant(s) can the net magnetic field be zero?
a) 1, 3
2
1
b) 2, 4
i
c) 1, 2, 3, 4
3
d) none
4
i
 
10. Consider the magnitude of  B . d  for the closed counter-clockwise paths 1, 2, 3 and 4 below.
 
4
The path for which  B . d  is biggest is:
9A in
a) 1
b) 2
4A out
5A out
1
c) 3
3
d) 4
2
8