Question

Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field.

Answer 1

Consider the simple case when a rectangular loop is placed in a uniform magnetic field B that is in the plane of the loop.

Force on arm AB = F₁ = IbB (directed into the plane of the loop)

Force on arm CD = F₂ = IbB (directed outward the plane of the loop)

Therefore, the magnitude of the torque on the loop due to these pair of forces is

τ = `F_1 a/2 + F_2 a/2`

= I(ab)B

= IAB

= mB

(A = ab = area of the loop)

Alternatively,

Also, accept if the student obtains the result.

Torque = IAB sin θ