Page 282 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 23] ELECTRICITY 267

where q 1 and q 2 are the magnitudes of the charges, r is the distance between them, and k is a constant whose
value in free space is

2
9
k = 9.0 × 10 N·m /C 2
The value of k in air is slightly greater. The constant k is sometimes replaced by
1
k =
4πε 0
where ε 0 , the permittivity offree space, has the value
2
2
ε 0 = 8.85 × 10 −12 C /(N·m )
(ε is the Greek letter epsilon.)

SOLVED PROBLEM 23.1
An electric charge Q is placed on a metal object. How does the charge distribute itself on the object?

Metals are good conductors of electricity, so the mutual repulsions of the individual charges that make up Q
cause them to spread out over the object’s surface in order to be as far apart as possible.

SOLVED PROBLEM 23.2

(a) When two objects attract each other electrically, must both be charged? (b) When two objects repel
each other electrically, must both be charged?

(a) No. A charged object can produce a separation of charge in a nearly uncharged object because atomic electrons
can shift around to some extent even without leaving their parent atoms. Figure 23-1 shows how a comb that
has been given a negative charge by being run through someone’s hair affects a small bit of paper. Electric
forces vary inversely with distance. Hence the attraction between the comb and the adjacent positive charges
in the paper is greater than the repulsion between the comb and the more distant negative charges. As a result,
the paper moves toward the comb. Only a small amount of charge separation can occur in this way, and so only
very light objects can be picked up; the charge separation in Fig. 23-1 is greatly exaggerated.
(b) Yes.

Fig. 23-1

SOLVED PROBLEM 23.3
An iron atom has 26 protons in its nucleus. (a) How many electrons does this atom contain? (b)How
many electrons does the Fe 3+ ion contain?