Page 336 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 27] MAGNETISM 321

SOLVED PROBLEM 27.4
Two parallel wires 10 cm apart carry currents of 8 A in opposite directions. What is the magnetic field
halfway between them?
Here the magnetic fields of the two currents are in the same direction and hence add. Since s = 5cm = 5×10 −2 m
halfway between the wires, the field of each current there is

−7
µ 0 I (4π × 10 T·m/A)(8A) −5
B = = = 3.2 × 10 T
2π s (2π)(5 × 10 −2 m)
and the total field is 2B = 6.4 × 10 −5 T.

MAGNETIC FIELD OF A CURRENT LOOP

The magnetic field at the center of a current loop of radius r has the magnitude

µ I
B = current loop
2 r
The field lines of B are perpendicular to the plane of the loop, as shown in Fig. 27-2(a). To find the direction
of B, grasp the loop so the curled fingers of the right hand point in the direction of the current; the thumb of that
hand then points in the direction of B [Fig. 27-2(b)].

r
I

(a) (b)
Fig. 27-2

A solenoid is a coil consisting of many loops of wire. If the turns are close together and the solenoid is long
compared with its diameter, the magnetic field inside it is uniform and parallel to the axis with magnitude
N
B = µ I solenoid
L
In this formula N is the number of turns, L is the length of the solenoid, and I is the current. The direction of B
is as shown in Fig. 27-3.

Fig. 27-3