Page 338 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 27] MAGNETISM 323

MAGNETIC FORCE ON A MOVING CHARGE
The magnetic force on a moving charge Q in a magnetic field varies with the relative directions of v and B.If
the angle between v and B is θ, as in Fig. 27-5(a), the force is
F = Qv B sin θ

When v is parallel to B, θ = 0 and sin θ = 0, so
F = 0 v || B

◦
When v is perpendicular to B, as in Fig. 27-5(b), θ = 90 and sin θ = 1, so
F = Qv B v ⊥ B

The direction of F in the case of a positive charge is given by the right-hand rule, shown in Fig. 27-5(c); F is in
the opposite direction when the charge is negative.

F F F
q

+Q + +Q +
v v
B B
v B

(a) (b) (c)
Fig. 27-5

MAGNETIC FORCE ON A CURRENT
Since a current consists of moving charges, a current-carrying wire will experience no force when parallel to a
magnetic field B and maximum force when perpendicular to B. In the latter case, F has the value

F = IL B I ⊥ B

where I is the current and L is the length of wire in the magnetic field. The direction of the force is as shown in
Fig. 27-6. In the general case, when the angle between I and B is θ, F = IL B sin θ.
Owing to the different forces exerted on each of its sides, a current loop in a magnetic field always tends to
rotate so that its plane is perpendicular to B. This effect underlies the operation of all electric motors.

F
I
L
Current
Force S N
B

Magnetic
field

Fig. 27-6