Solutions to Homework Questions 1

Physics 112 Homework 1 (solutions) (2004 Fall)
Chapt15, Problem-28: Figure P15.28 shows
the electric field lines for two point charges separated
by a small distance. (a) Determine the ratio q 1 /q 2 . (b)
What are the signs of q 1 and q 2 ?
Solution:
The magnitude of q 2 is three times the magnitude of q 1
because 3 times as many lines emerge from q 2
as enter q 1 . q 2 = 3 q 1
(a) Then, q 1 q 2 =−1 3
(b)
q 2 > 0 because lines emerge from it,
and q 1 < 0 because lines terminate on it
Chapt15, Problem-35: If the electric field strength in air exceeds 3.0 x 10 6 N/C, the air becomes a
conductor. Using this fact, determine the maximum amount of charge that can be carried by a metal sphere
2.0 m in radius.
Solution:
For a uniformly charged sphere, the field is strongest at the surface.
Thus, E max = k e q max
R 2 ,
or
q max = R2 E max
k e
( )
( = 2.0 m)2
3.0 ×10 6 N C
8.99 ×10 9 N⋅ m 2 C 2 = 1.3 ×10 −3 C
Chapt15, Problem-41: A 40-cm-diameter loop is rotated in a uniform electric field until the
position of maximum electric flux is found. The flux in this position is measured to be 5.2 x 10 5 N · m 2 /C.
Calculate the electric field strength in this region.
Solution:
From the definition of Electric Flux Φ E = EAcosθ and Φ E = Φ E, max when θ = 0°
Thus, E = Φ E, max
A
( )
= Φ E, max
πd 2 4 = 4 5.2 ×105 N⋅ m 2 C
π 0.40 m
( ) 2 = 4.1× 106 N C
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