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Example for Electricity Section "Phys 106"
1. Two balls each having a charge of 3 µC are separated by 20 mm. What is the
force of repulsion between them?
Solution
(9 x 109 N ⋅ m 2 /C 2 )(3 x 10-6 C)(3 x 10-6C)
F=
; F = 202 N
(20 x 10-3m) 2
2. Two point charges of -3 and +4 µC are 12 mm apart in a vacuum. What is the
electrostatic force between them?
Solution
(9 x 109 N ⋅ m 2 /C 2 )(−3 x 10-6C)(4 x 10-6C)
F=
; F = 750 N, attraction
(12 x 10-3m) 2
3. What is the separation of two -4 µC charges if the force of repulsion between
them is
200 N?
Solution
r=
kqq '
(9 x 109 N ⋅ m 2 /C 2 )(−4 x 10-6C)2
=
;
F
200 N
r = 26.8 mm
4. Two identical charges separated by 30 mm experience a repulsive force of 980 N.
What is the magnitude of each charge?
Solution
kq 2
Fr 2
(980 N)(0.030 m)2
F = 2 ; q=
=
;
q = 9.90 µC
r
k
9 x 109 N ⋅ m 2 /C 2
5. A +8-nC charge is placed at a point P, 40 mm from a +12-µC charge. What is
the potential energy per unit charge at point P in joules per coulomb?
Will this change if the 8-nC charge is removed?
Solution
kQq (9 x 109 N ⋅ m 2 /C2 )(+12 x 10-6C)(8 x 10−9C)
P .E. =
=
r
0.040 m
P.E. = 0.0216 J;
V=
P .E. 0.0270 J
=
;
q
8 x 10-9 C
V = 2.70 x 106 J/C;
No
The P.E./q is a property
of space. If another charge were placed there or if no charge were there, the
P.E./q is the same.
6. A charge of +6 µC is 30 mm away from another charge of 16 µC. What is the
potential energy of the system?
Solution
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kQq (9 x 109 N ⋅ m 2 /C2 )(+6 x 10-6C)(16 x 10−6C)
P . E. =
=
;
r
0.030 m
P.E. = 28.8 J
7. A 28-µF parallel-plate capacitor is connected to a 120-V source of potential
difference. How much charge will be stored on this capacitor?
Solution
Q = CV = (28 µF)(120 V);
Q = 3.36 mC
8. A potential difference of 110 V is applied across the plates of a parallel-plate
capacitor. If the total charge on each plate is 1200 µC, what is the
capacitance?
Solution
Q 1200 µ C
C= =
;
C = 10.9 µF
V
110 V
9. What is the potential energy stored in the electric field of a 200-µF capacitor
when it is charged to a voltage of 2400 V?
Solution
P .E. = ½CV 2 = ½(200 x 10-6 F)(2400 V) 2 ; P.E. = 576 J
10. 10. A parallel plate capacitor has a plate area of 4 cm2 and a separation of 2
mm. A dielectric of constant K = 4.3 is placed between the plates, and the
capacitor is connected to a 100-V battery. How much energy is stored in the
capacitor?
Solution
A (4.3)(8.85 x 10-12 C2 /N ⋅ m 2 )(4 x 10-4 m 2 )
C = Kε 0 =
; C = 7.61 pF
d
0.002 m
P.E. = ½CV2 = ½(7.61 x 10-12 F)(100 V)2;
P.E. = 3.81 x 10-8 J
11. What is the potential drop across a 4-Ω resistor with a current of 8 A passing
through it?
Solution
V = IR = (8 A)(4 Ω); V = 32.0 V
12. Find the resistance of a rheostat if the drop in potential is 48 V and the
current is 4 A.
Solution
V 48 V
R= =
;
R = 12.0 Ω
I
4A
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13. An electric lamp has an 80-Ω filament connected to a 110-V direct-current
line. What is the current through the filament? What is the power loss in
watts?
Solution
V 110 V
;
I= =
I = 1.38 A
R 80 Ω
P=
V 2 (110 V)2
=
;
R
80 Ω
P = 151 W
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