Page 284 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 23] ELECTRICITY 269

Since the proton mass is 1.67 × 10 −27 kg, the gravitational force between two protons that are a distance r
apart is
2
2
Gm 1 m 2 (6.67 × 10 −11 N·m /kg )(1.67 × 10 −27 kg) 2 1.86 × 10 −64 2
F grav = = = N·m
r 2 r 2 r 2
The electric force between the protons is
2
2
9
(9 × 10 N·m /C )(1.6 × 10 −19 C) 2 2.3 × 10 −28
kq 1 q 2 2
F elec = = = N·m
r 2 r 2 r 2
At every separation r, the electric force between the protons is greater than the gravitational force between them by
36
a factor of more than 10 ; the forces are never equal.
SOLVED PROBLEM 23.9
A test charge of +1 × 10 −6 C is placed halfway between a charge of +5 × 10 −6 C and a charge of
+3 × 10 −6 C that are 20 cm apart (Fig. 23-2). Find the magnitude and direction of the force on the test
charge.

Fig. 23-2

The force exerted on the test charge q by the charge q 1 is
2
2
9
(9 × 10 N·m /C )(1 × 10 −6 C)(5 × 10 −6 C)
kqq 1
F 1 = = =+4.5N
r 2 (0.1m) 2
1
This force is taken to be positive because it acts to the right. The force exerted by the charge q 2 on q is
9
2
2
(9 × 10 N·m /C )(1 × 10 −6 C)(3 × 10 −6 C)
kqq 2
F 2 = = =−2.7N
r 2 (0.1m) 2
2
This force is taken to be negative because it acts to the left. The net force on the test charge q is
F = F 1 + F 2 =+4.5N − 2.7N =+1.8N
and it acts to the right, that is, toward the +3 × 10 −6 C charge.
ELECTRIC FIELD
An electric field is a region of space in which a charge would be acted upon by an electric force. An electric field
may be produced by one or more charges, and it may be uniform or it may vary in magnitude and/or direction
from place to place.
If a charge q at a certain point is acted on by the force F, the electric field E at that point is defined as the
ratio between F and q:

F
E =
q
force
Electric field =
charge
Electric field is a vector quantity whose direction is that of the force on a positive charge. The unit of E is the
newton per coulomb (N/C) or, more commonly, the equivalent unit volt per meter (V/m).