Page 337 - Schaum's Outline of Theory and Problems of Applied Physics

322 MAGNETISM [CHAP. 27

SOLVED PROBLEM 27.5
A 100-turn flat circular coil has a radius of 5 cm. Find the magnetic field at the center of the coil when
the current is 4 A.
Each turn of the coil acts as a separate loop in contributing to the total magnetic field. If there are N turns, the
result is a field N times stronger than each turn produces by itself. Hence

−7
µ 0 NI (4π × 10 T·m/A)(100)(4A) −3
B = = = 1.6 × 10 T
2π r (2π)(5 × 10 −2 m)

EARTH’S MAGNETIC FIELD
The earth has a magnetic field that arises from electric currents in its liquid iron core. The field is like that which
would be produced by a current loop centered a few hundred miles from the earth’s center whose plane is tilted
◦
by 11 from the plane of the equator (Fig. 27-4). The geomagnetic poles are the points where the magnetic axis
passes through the earth’s surface. The magnitude of the earth’s magnetic field varies from place to place; a
typical sea-level value is 3 × 10 −5 T.

Fig. 27-4

SOLVED PROBLEM 27.6
A solenoid 0.2 m long has 1000 turns of wire and is oriented with its axis parallel to the earth’s magnetic
field at a place where the latter is 2.5 × 10 −5 T. What should the current in the solenoid be in order that
its field exactly cancel the earth’s field inside the solenoid?
The magnetic field inside an air-core solenoid is
N
B = µ 0 I
L
3
Here N = 10 , L = 0.2m,and B = 2.5 × 10 −5 T, so
BL (2.5 × 10 −5 T)(0.2m)
I = = = 0.004 A
3
µ 0 N (4π)(10 −7 T·m/A)(10 )