Page 339 - Schaum's Outline of Theory and Problems of Applied Physics

324 MAGNETISM [CHAP. 27

FORCE BETWEEN TWO CURRENTS
Two parallel electric currents exert magnetic forces on each other (Fig. 27-7). If the currents are in the same
direction, the forces are attractive; if the currents are in opposite directions, the forces are repulsive. The force
per unit length F/L on each current depends on currents I 1 and I 2 and their separation s:
F µ 0 I 1 I 2
= parallel currents
L 2π s

F F
I 1 I 1

L s L

I 2 I 2
F F
Fig. 27-7

SOLVED PROBLEM 27.7
A positive charge is moving virtually upward when it enters a magnetic field directed to the north. In
what direction is the force on the charge?
To apply the right-hand rule here, the fingers of the right hand are pointed north and the thumb of that hand is
pointed upward. The palm of the hand faces west, which is therefore the direction of the force on the charge.

SOLVED PROBLEM 27.8

A proton is moving in a uniform magnetic field. Describe the path of the proton if its initial direction is
(a) parallel to the field, (b) perpendicular to the field, and (c) at an intermediate angle to the field.
(a) There is no magnetic force on the proton, so it continues to move in a straight line [Fig. 27-8(a)].
(b) The force on the proton is perpendicular to it velocity v and also perpendicular to B; hence it moves in a circle,
as in Fig. 27-8(b).
(c) The proton moves in the helical path of Fig. 27-8(c) because the component of v parallel to B is not changed
while the component of v perpendicular to B leads to an inward force, as in (b).

B

(a) (b) (c)
Fig. 27-8

SOLVED PROBLEM 27.9
A charged particle moving perpendicular to a uniform magnetic field follows a circular path. Find the
radius of the circle.