Question

(a) Derive the expression for the torque acting on a current carrying loop placed in a magnetic field.
(b) Explain the significance of a radial magnetic field when a current carrying coil is kept in it.

Answer 1

The torque is τ = m x B

Explanation:

Consider a loop ABCD.

Let the current through the loop be I.

The force acting on the arms BC and AD are equal and opposite. Also, they are collinear. Hence, they produce no torque.

Now, consider force F1 and F2 on arms AB And CD respectively.

F1 = F2 = IbB

The net torque is given by:

τ = F1 a/2 sinθ + F2 a/2 sinθ  = LabBsinθ  = laBsinθ

Magnetic moment of loop is given by:

m = I A

We can say that the angle between m and B is θ.

Thus

τ = m x B

(b)  τ = IABsinθ

A radial magnetic field ensures that the angle  is always 90° irrespective of the rotation of the coil. Hence, the torque is always maximum even if the coil rotates.

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Answer 2

Answer:

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