Question

A rectangular loop of wire of dimension 12 cm 25 cm faces a long, straight wire. The two long sides of the loop are parallel to the wire, and the two short sides are perpendicular; the midpoint of the loop is 8.0 cm from the wire (Fig. 30.33). Currents of 95 A and 70 A flow in the straight wire and the loop, respectively. (a) What translational force does the straight wire exert on the loop? (b) What torque about an axis parallel to the straight wire and through the center of the loop does the straight wire exert on the loop?

Answer 1

a) zero.

Beacsue the stright wire exerts equal force on upper and lower segments of rectangular loop but in opposite direction.

net froce becomes zero.

b) Let L = 25 cm = 0.25 m

distance between staright wire to upper(or lower) segment,

d = sqrt(8^2 + 6^2)

= 10 cm

= 0.1 m

magnetic Force acting on the upper and lower segments,

F = mue*I1*I2*L/(2*pi*d)

= 4*pi*10^-7*95*70*0.25/(2*pi*0.1)

= 0.0033 N

angle made by F with vertical, theta = tan^-1(8/6)

= 53.13 degrees

so, Torque due to manetic force, T = 2*r*F*sin(theta)

= 2*0.06*0.0033*sin(53.13)

= 3.17*10^-4 N.m (Answer)

I hope help you !!