Physics

Problem

A straight steel wire is placed in a uniform magnetic field. When the wire makes an angle of

30^{\circ}

with the field, the magnitude of the magnetic force on it is

F_1

. When the wire is rotated so that it makes an angle of

60^{\circ}

with the same field, the force becomes

F_2

. Assume that the current

I

, the length

L

, and the magnetic field strength

B

remain unchanged during rotation. a. (i) Establish a mathematical relationship between

F_1

and

F_2

. b. (ii) Find the numerical ratio

\dfrac{F_1}{F_2}

. c. (iii) Determine the angle

\theta

(with

0^{\circ} \le \theta \le 90^{\circ}

) for which the magnitude of the force equals the arithmetic mean of

F_1

and

F_2