A rectangular coil of effective area 0.04 m 2 is suspended freely in a radial magnetic field of 0.02 Wb/m 2 . The torsional constant of the suspension fibre is 5 × 1 0 − 9 Nm/degree . If a current of

Question

A rectangular coil of effective area 0.04 m 2 is suspended freely in a radial magnetic field of 0.02 Wb/m 2 . The torsional constant of the suspension fibre is 5 × 1 0 − 9 Nm/degree . If a current of 250 μ A is passed through it, then the angle through which it rotates is

TestHub · Accepted Answer

For a coil in a radial magnetic field, the deflecting torque is given by

$τ_{d} = I A_{e ff} B$

The restoring torque provided by the suspension fibre is

$τ_{r} = Cθ$

In equilibrium, $τ_{d} = τ_{r}$

$I A_{e ff} B = Cθ$

$θ = \frac{I A _{e ff} B}{C}$

Substituting the given values:

$θ = \frac{250 \times 1 0 ^{- 6} \times 0.04 \times 0.02}{5 \times 1 0 ^{- 9}}$

$θ = \frac{2 \times 1 0 ^{- 7}}{5 \times 1 0 ^{- 9}}$

$θ = 4 0^{\circ}$

Answer: $4 0^{\circ}$

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