Page 335 - Schaum's Outline of Theory and Problems of Applied Physics

320 MAGNETISM [CHAP. 27

MAGNETIC FIELD OF A STRAIGHT CURRENT
An electromagnetic field surrounds every electric charge. The electric part is always present, but the magnetic
part only appears when there is relative motion. In the case of a wire that carries an electric current, only a
magnetic field is present around it because the wire is electrically neutral. The electric fields of the electrons
in the wire are canceled out by the opposite electric fields of the positive ions, but the ions are stationary and
produce no magnetic fields to cancel out the magnetic fields of the moving electrons. If we just move a wire with
no current in it, the electric and magnetic fields of the electrons are canceled out by the opposite electric and
magnetic fields of the positive ions.
The magnetic field a distance s from a long, straight current I has the magnitude

µ I
B = straight current
2π s
where µ is the permeability of the medium in which the magnetic field exists. The permeability of free space µ 0
has the value
µ 0 = 4π × 10 −7 T·m/A = 1.257 × 10 −6 T·m/A
The value of µ in air is very nearly the same as µ 0 and is usually considered as equal to µ 0 .
The field lines of the magnetic field around a straight current are in the form of concentric circles around the
current. To find the direction of B, place the thumb of the right hand in the direction of the current; the curled
fingers of that hand then point in the direction of B (Fig. 27-1).
B
s
I

Fig. 27-1

SOLVED PROBLEM 27.1
In what ways are electric and magnetic fields similar? In what ways are they different?
Similarities: Both fields originate in electric charges, and both fields can exert forces on electric charges.
Differences: All electric charges give rise to electric fields, but only a charge in motion relative to an observer
gives rise to a magnetic field. Electric fields exert forces on all charges, but magnetic fields exert forces only on
moving charges.

SOLVED PROBLEM 27.2
A cable 5 m above the ground carries a current of 100 A from east to west. Find the direction and magnitude
of the magnetic field on the ground directly beneath the cable. (Neglect the earth’s magnetic field.)
From the right-hand rule, the direction of the field is south. The magnitude of the field is
−7
µ 0 I (4π × 10 T·m/A)(100 A) −6
B = = = 4 × 10 T
2π s (2π)(5m)
SOLVED PROBLEM 27.3

Two parallel wires 10 cm apart carry currents of 8 A in the same direction. What is the magnetic field
halfway between them?

The magnetic field halfway between the wires is zero because the fields of the currents are opposite in direction
and have the same magnitude there.