Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 1
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 1
Q1.
A metal plate is connected by a conducting wire to the ground through a switch as
shown in FIGURE 1. The switch is initially closed. A charge +Q is brought close to
the plate without touching it, and then the switch is opened. What is the charge on the
plate after the switch is opened and the charge +Q is removed?
A) −Q
B) +Q
C) 0
D) −Q/2
E) −2Q
Ans:
A
Q2.
Two small identical metal spheres with negligible mass carry charges q1 and q2 with
opposite sign of charges such that │q1│> │q2│. When the charges are separated by a
distance of 1.0 m, they experience a 2.5 N attractive force. Both charges are then
brought in physical contact till the electrostatic equilibrium is reached among the two
spheres. Finally they are separated from each other and placed at a distance of 1.0 m
apart. Now they experience a 2.5 N repulsive force. What were the magnitudes of the
original charge q1 and q2 respectively?
A) 40.2 C, 6.90 C
B) 50.2 C, 13.7 C
C) 4.51 C, 2.85 C
D) 15.5 C, 9.67 C
E) 59.7 C, 10.5 C
Ans:
F1 = kq1q2
d2; F2 =
k(q1 − q2)2
d2; q1q2 =
F1𝑑2
𝑘; q1 − q2 = √
F2𝑑2
𝑘
q1q2 = 2.777 × 10−10C2; q1 − q2 = 3.333 × 10−5 C; q1 − q2 + 3.333 × 10−5 C
q1q2 = q2 (q2 + 3.333 × 10−5) = 2.777 × 10−10 C2
𝑞22 + 3.333 × 10−5q2 − 2.777 × 10−10 = 0; q2 = 0.690 × 10−5 𝐶; 4.02 × 10−5 𝐶
q1 = 0.691 × 10−5 + 3.333 × 10−5𝐶 = 4.0233 × 10−5 𝐶
Figure 1
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 2
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q3.
Three identical 1.0 nC positive point charges are placed as shown in FIGURE 2. Find
the magnitude of the resultant electric field due to these three charges at a point P
located 3.0 cm in front of the middle charge.
A) 27 kN/C
B) 15 kN/C
C) 11 kN/C
D) 37 kN/C
E) 45 kN/C
Ans:
θ = tan−1 (1
3) = 18.44° ; Ep = Ex + 2E′cosθ = kq [
1
(0.03)2+
2cosθ
(0.0316)2]
Ep = 9 × 109 × 10−9[1111.1 + 1900.5] = 27104 𝑉/𝑚 = 27 𝑘𝑉/𝑚
Q4.
A proton is shot in a region with a speed 2.0 ×106 m/s making an angle of 30o with +
x-axis. If an electric field E = −112 i kN/C exists in the region, then how far does
the proton travel along the x-axis before reaching its turning point?
A) 14 cm
B) 11 cm
C) 5.1 cm
D) 25 cm
E) 22 cm
Ans:
|𝑎| =𝑞𝑒𝐸
𝑚𝑝=
1.6 × 10−19 × 112 × 103
1.67 × 10−27= 1.07 × 1013𝑚/𝑠
v0𝑥 = v0𝑐𝑜𝑠30 = 2 × 106 × cos 30
𝑇ℎ𝑒𝑛 v 𝑓𝑥2 = 𝑣𝑜𝑥
2 + 2|𝑎|𝑥 ; v𝑓𝑥 = 0
𝑇ℎ𝑒𝑛 𝑥 =v𝑜𝑥
2
2|𝑎|=
(2 × 106 × 𝑐𝑜𝑠30)2
2 × 1.07 × 1013=
3 × 102
2 × 1.07 × 1013= 0.14 𝑚
1.0 cm
1.0 cm
3.0 cm
1.0 nC
1.0 nC
1.0 nC
P
X-axis
Y-axis
𝐸′
𝜃
𝐸𝑥
𝐸′
𝜋
10
Figure 2
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 3
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q5.
Rank the potential energies U of four electric dipoles in a uniform electric field E
shown in FIGURE 3 from most positive to most negative.
A) a, c and d tie, b
B) b, a and d tie, c
C) c, b, a and d tie
D) d, a, c and b tie
E) a, c and b tie, d
Ans:
𝑈 = −p ∙ E = −pEcosθ
Ua = −pEcos135° = 0.71 pE
Ub = −pEcos0° = − pE
Uc = −pEcos90° = 0
Ud = −pEcos270° = 0
a, c and d tie, b
Q6.
A point charge located at the origin generates an electric field of magnitude 1.25 × 106
N/C at a point located at a distance of 0.150 m from the origin. What is the electric flux
through the surface of a sphere of 0.150 m radius centered at the origin?
A) 3.53 × 105 N.m2/C
B) 1.22 × 105 N.m2/C
C) 0.97 × 105 N.m2/C
D) 4.55 × 105 N.m2/C
E) 5.11 × 105 N.m2/C
Ans:
ϕ = EA = 1.25 × 106 × 4π(0.15)2 = 3.53 × 105 N ∙ m2/C
a b c d
E
E
E
Figure 3
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 4
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q7.
An infinitely wide uncharged conducting metal plate is located in horizontal plane
parallel to an infinitely wide insulating sheet of charge, as shown in FIGURE 4. The
sheet and the metal plate are a distance d apart and the sheet has positive surface charge
density +. What is induced surface charge density on the lower side of the conductor
facing the sheet?
A) /2
B) +/2
C)
D) +
E) 2
Ans:
For lower surface E = σ′
εo
E is due to the sheet , E =σ
2εo
Then E = σ′
εo=
σ
2εo
σ′ = σ
2
Q8.
An infinitely long line of negative charge has a linear charge density C/m and lies
parallel to the y-axis at x = −2.00 m. A positive point charge of magnitude 1.50 C is
located at x =1.00 m and y = 2.00 m. If the magnitude of the x-component of the
resultant electric field at x = 2.00 m and y = 2.00 m is 4.95 × 103 V/m, what is magnitude
of the charge density ?
A) 1.90 × 10-6 C/m
B) 2.31 × 10-6 C/m
C) 0.39 × 10-6 C/m
D) 5.33 × 10-5 C/m
E) 1.00 × 10-5 C/m
Ans:
E𝑝 = 𝐸𝜆 + 𝐸𝑞 = 2𝑘𝜆
4+
𝑘𝑞
(1)2= 4.95 × 103
𝑘𝜆
2+ 𝑘𝑞 = 4.95 × 10−3: 𝜆 = 2 [
4.95 × 10−3
𝑘− 𝑞]
𝜆 = 2
𝑘[4.95 × 103 − 𝑘𝑞] = 2 [
4.95 × 103
9 × 109− 1.5 × 10−6] = −1.90 × 10−6 𝑐/𝑚
Conductor
Conductor lower side
Sheet Sheet surface charge
density +σ
d
𝜎′
Figure 4
E E
q p
C/m
-2m
2m
1 m
(2, -2)
X
Y
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 5
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q9.
The electric field at a distance of 0.145 m from the surface of a solid insulating sphere
with radius 0.355 m is 1750 N/C. Assuming the sphere’s charge is uniformly
distributed, what is the electric field inside the sphere at a distance of 0.200 m from
the center?
A) 1.96 × 103 N/C
B) 1.10 × 103 N/C
C) 0.55 × 103 N/C
D) 2.45 × 103 N/C
E) 3.33 × 103 N/C
Ans:
For insulating sphere Er(r > R) = kQ
r2;
Er(r < R) = kQ
R3∙ 𝑟
𝐹𝑜𝑟 𝑟 > 𝑅, 𝐸 (𝑟 > 𝑅) = 1750 =kQ
(0.355 + 0.145)2=
kQ
(0.5)2
⇒ kQ = (0.5)2 × 1750 = 437.5
𝐹𝑜𝑟 𝑟 < 𝑅, 𝐸 (𝑟 < 𝑅) = 𝑘𝑄
𝑅3∙ 𝑟
E′(𝑟 < 𝑅) = 437.5
(0.355)3× 0.2 = 1955.8 𝑁/𝐶 = 1.96 × 103 𝑁/𝐶
Q10.
A proton is placed midway between points A and B. The potential at point A is –20
V, and the potential at point B is + 20 V. The potential at the mid-point is 0 V. The
proton will
A) accelerate toward point A
B) move toward point B with constant velocity
C) accelerate toward point B
D) move toward point A with constant velocity
E) remain at rest
Ans:
B
+20
A
-20
+
E
V= 0
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 6
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q11.
An insulating sheet in the XZ plane is uniformly charged with a positive surface charge
density = 3.50 × 10-6C/m2, as shown in FIGURE 5. What is the change in the
potential energy of a point charge Q = 13.6 C when it is moved from point A to point
B.
A) 2.69 J
B) 1.15 J
C) 1.78 J
D) 4.11 J
E) 5.22 J
Ans:
∆y = 2 − 3 = −1 m
∆V = −𝐸𝑦∆y = −𝜎
2𝜀𝑜 × (−1) =
−3.5 × 10−6 × (−1)
2 × 8.85 × 10−12= 197740.1
∆U = q∆V = 13.6 × 10−6 × 197740.1 = 2.689 J
Q12.
Four 1.0-g spheres, each carrying a charge of 5.0 nC, as shown in FIGURE 6, are held
fixed in their positions. They are then released at the same time and allowed to move
away from each other. What is the speed of each sphere when they are very far apart?
Assume the electric potential V = 0 at infinity.
A) 0.11 m/s
B) 1.9 m/s
C) 0.14 m/s
D) 0.02 m/s
E) 2.2 m/s
Ans:
∆U = 4(1
2𝑚v2) = 2 𝑚v2
∆U = 4𝑘𝑞2
0.05+
2𝑘𝑞2
0.0707= 2𝑘𝑞2 [
2
0.05+
1
0.0707]
= 2 × 9 × 109 × (5 × 10−9)2[40 + 14.14] = 2.44 × 10−5
v = √∆𝑈
2𝑚 = √
2.44 × 10−5
2 × 10−3 = 0.11 𝑚/𝑠
Figure 6
Ey 𝐸𝑦
𝐸𝑦 𝑦
Figure 5
50
7.05
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 7
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q13.
FIGURE 7 shows two uniformly charged spheres having charges of 100 nC and 25 nC
and separated by a center-to-center distance of 100 cm. What is the potential difference
between points a and b, i.e. Vba? Note that points a and b are located on the surfaces of
the larger and smaller spheres, respectively. Assume V = 0 at infinity.
A) 2.1 kV
B) 1.0 kV
C) 1.5 kV
D) 3.2 kV
E) 4.4 kV
Ans:
Vba = Vb − Va ;
Vb = k [qa
0.95+
qb
0.05] = 9 × 109 [
100
0.95+
25
0.05] × 10−9 = 5447.34 V
Va = k [qa
0.3+
qb
0.7] = 9 × 109 [
100
0.3+
25
0.7] × 10−9 = 332.14 V
Vba = Vb − Va = 5447.3 − 3321.4 = 2125.9 V = 2.13 × 103 V
100 nC
60 cm
100 cm
10 cm
25 nC a b
Figure 7
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 8
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q14.
Six identical capacitors with capacitance C = 5 F are connected to a power supply
V= 12 V as shown in FIGURE 8. What is the equivalent capacitance of these six
capacitors and what is the potential difference Vab between points a and b ?
A) 7.5 F ; 0.0 V
B) 1.5 F ; 9.0 V
C) 9.7 F ; 6.5 V
D) 3.3 F ; 2.0 V
E) 12 F ; 0.0 V
Ans:
Ceq = 3 C
2= 3 ×
5
2= 7.5 μF
Vb = Va Vb − Va = 0
Figure 8
⇒ ⇒ V
C C C
C C C
b a
C/2 C/2 V C/2 V 𝐶𝑒𝑞
⇒
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 9
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q15.
In FIGURE 9, V = 12 V, C1 = C5 = C6 =6.0 F, and C2 = C3 = C4 = 4.0 F. What is the
charge stored on the capacitor C1 and C5?
A) 48 C , 0 C
B) 16 C, 32 C
C) 22 C, 12 C
D) 65 C, 0 C
E) 16 C, 10 C
Ans:
Ceq = C1 × C234
C1 + C234 where C234 = C2 + C3 + C4 = (4 + 4 + 4)μF = 12μF
Ceq = 6 × 12
6 + 12 μF = 4μF
Q1 = Ceq × V = 4 μF × 12 = 48 μC
Q5 = 0 μC (short circuit)
Figure 9
𝑪𝟐 𝑪𝟑 𝑪𝟒
𝑪𝟏
𝑽
V 𝐶𝑒𝑞
⟹ ⟹
Short Circuit
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 10
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q16.
An air capacitor made of two flat square plates, each with area A = 100 cm2 and
separated by a distance d = 10.0 cm, is connected across a 150 V battery. Then a metal
square slab having thickness a = 5.00 cm and area A = 100 cm2 is inserted in the
middle of the air gap between the plates without touching either plate, as shown in
FIGURE 10. What is the energy stored in the circuit now?
A) 20.0 nJ
B) 25.0 nJ
C) 33.3 nJ
D) 15.7 nJ
E) 10.1 nJ
Ans:
C = ε0
A
(d − a
2 )=
8.85 × 10−12 × 100 × 10−4
(10 − 5
2 ) × 10−12= 3.54 × 10−12F
Ceq = C
2=
3.54 × 10−12
2= 1.77 × 10−12μF
𝑈 =1
2 𝐶𝑒𝑞𝑉
2 = 1
2× 1.77 × 10−12 × (150)2 = 1.99 × 10−8 J = 1.99 × 10−9 J
a d
Figure 10
C
C
150 V 𝐶𝑒𝑞 150 V ⇒ ⇒
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 11
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q17.
Two parallel plate capacitors C1 and C2 are connected in series to a 96.0 V battery. Both
capacitors have plates with an area of 1.00 cm2 each and a separation of 0.100 mm. C1
has air between the plates and C2 has that space filled with porcelain with a dielectric
constant =7. If the capacitors are connected across the battery for a long time, what is
the charge on capacitor C1?
A) 0.74 nC
B) 1.52 nC
C) 0.52 nC
D) 0.24 nC
E) 2.55 nC
Ans:
Equivalent capacitance C1 = ε0
A
d=
8.85 × 10−12 × 10−4
0.1 × 10−3= 8.85 × 10−12 F
C2 = κ ∙ C1
Ceq = C1 × κC1
C1 + κC1=
κ ∙ C1
κ + 1=
7
8 C1 =
7
8 × 8.85 × 10−12 F = 7.74 × 10−12 F
𝑄𝑐1 = Ceq × V = 7.74 × 10−12 F × 96 = 0.74 × 10−9 C
Q18.
At what temperature will tungsten have a resistivity four times that of copper when
copper is at room temperature (20C)? ( tungsten-room-temp = 5.6 ×10-8 .m; tungsten = 4.5
× 10-3( C)-1 Cu-room-temp = 1.7 x 10-8 .m)
A) 67.6 C
B) 89.1 C
C) 33.2 C
D) 12.2 C
E) 99.5 C
Ans:
ρTung(T) = ρcu−RT (1 + αTungsten∆T) ∆T = (ρTung(T)
ρCu−RT− 1) ×
1
αTung
∆T = (4 × 1.7 × 10−8
5.6 × 10−8− 1) ×
1
4.5 × 10−3= 47.55 C
𝑇𝑓 = 𝑇𝑖 + ∆T = 20 + 47.55 = 67.55℃
Phys102 Second Major-153 Zero Version
Coordinator: Dr. A. Naqvi Thursday, August 18, 2016 Page: 12
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0
Q19.
A copper wire joins an aluminum wire whose diameter is twice that of the copper wire.
The same current flows in both wires. The density of conduction electrons in copper
nCu=1.1×1029 m-3 and the density of conduction electrons in aluminum nAl=2.1 × 1029
m-3. For the two wires the drift speed ratio vd-Cu / vd-Al and the current density ratio
JCu/JAl respectively, are:
A) 7.6, 4.0
B) 3.7, 2.4
C) 1.5, 2.6
D) 11, 5.5
E) 9.6, 2.2
Ans:
nAqvd = I ; vd = I
nAq ;
vd−cu
vd−Al=
nAl × AAl
nCu × ACu
(IAl = ICu)
vd−Cu
vd−Al=
2.1 × 1029 × 4
1.1 × 1029 × 1
JCu
JAl=
IAl
ACu×
AAl
IAl=
AAl
ACu= 4
Q20.
A certain brand of hot-dog cooker applies a potential difference of 120 V to the opposite
ends of the hot-dog and cooks it by means of heat produced in the hot-dog. If 48.0 kJ
of heat is needed to cook each hot-dog, what current is needed to be supplied by the
120 V power supply to cook three hot-dogs simultaneously in 2 min? Assume the hot-
dogs form three resistors connected in parallel in the circuit.
A) 10.0 A
B) 8.22 A
C) 12.1 A
D) 5.72 A
E) 15.1 A
Ans:
𝐸𝑛𝑒𝑟𝑔𝑦 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑡𝑜 𝑐𝑜𝑜𝑘 3 ℎ𝑜𝑡 − 𝑑𝑜𝑔𝑠 = 3 × 48 × 103 J = 1.44 × 105 J
Time required to cook = 2 minutes
𝑃𝑜𝑤𝑒𝑟 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 (J
𝑠) =
1.44 × 105
120= 1200 𝑊
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑏𝑦 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 = 𝑃
𝑉=
1200
120= 10 𝐴