Question

A wire of length 74 cm is wound into a circular coil of 5 loops. The coil carries a current 1.4 A. Find the maximum torque on the coil in a uniform magnetic field of 2.3 T.

Answer 1

The torque on the coil can be find out by using

=N I B A sin -----------------(1)

From the above equation it is clear that we find the maximum torque when the value of should be 90^o

_max =N I B A ----------------(1)

here I = current in the coil = 1.4 A.

B = uniform magnetic field = 2.3 T.

A = area of the circular coil = r²   { r =radius of the circular coil }

N = number of loops = 5

It is given as wire of length 74 cm is wound into a circular coil of 5 loops, so

74 cm = 5 ( 2 r )

r = 2.3567 cm =  2.3567  x 10^-2 m.

The area of the coil A =   r² = (3.14) (2.3567  x 10^-2 m)² = 17.44 x 10^-4 m².

on substituting all values in (1) we get

_max =(5) (1.4 A) (2.3 T) (17.44 x 10^-4 m² )

_max = 280.784 x 10^-4 N.m

_max = 0.0281 N.m (approx)

Therefore the maximum torque on the coil is 0.0281  N.m.