A wire of length 17.6 cm carrying a current of 5.95 mA is to be formed into a circular coil and placed in a uniform magnetic field of magnitude 4.74 mT. The torque on the coil from the field is maximized. (a) What is the angle between and the coil's magnetic dipole moment? (b) What is the number of turns in the coil? (c) What is the magnitude of that maximum torque?

(a) the angle between the coil and the coil's magnetic dipole moment is same that means zero degree.

(b) L = 17.6 cm = 0.176 m

i = 5.95 mA = 5.95 x 106-3 A

B = 4.74 mT = 4.74 x 10^-3 T

(b) Let r be the radius of the loop is r

Circumference = 2 x 3.14 x r

0.176 = 2 x 3.14 x r

r = 0.028 m

B = μo/4π x (N x 2 π i) / r

Where, N be the number of turns

4.74 x 10^-3 = (10^-7 x N x 2 x 3.14 x 5.95 x 10^-3) / 0.028

N = 3.55 x 10^4

(c) Maximum torque = N i A B

τ = 3.55 x 10^4 x 5.95 x 10^-3 x 3.14 x 0.028 x 0.028 x 4.74 x 10^-3

τ = 2.465 x 10^-3 Nm