Question

The effective radius of a circular coil is R and
number of turns is N. The current through it is
i ampere. The work done is rotating the coil
from angle 0 = 0° to 0 = 180° in an external
magnetic field B will be -​

Answer 1

The effective radius of a circular coil is R and number of turns is N. The current through it is i ampere. The work done is rotating the coil from angle 0° to 180° in an external magnetic field B will be -

solution : first of all, find magnetic moment of circular coil.

magnetic moment, M = ANI

where A is area of circular coil, i.e., A = πR².

N is number of turns and I is current through wire.

so, magnetic moment, M = πR²Ni

given, magnetic field intensity is B

we know, workdone is rotating a coil from α to β in external magnetic field B is given by, W = MB(cosα - cosβ)

given, α = 0° and β = 180°

so, workdone , W = πR²NiB(cos0° - cos180°)

= πR²NiB(1 + 1) = 2πR²NiB