A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by against the torque is [2017]

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Solution

Q.
A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $μ A$ and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by $180 °$ against the torque is [2017]

1 4.55 $μJ$

2 2.3 $μJ$

3 1.15 $μJ$

4 9.1 $μJ$

Ans.
(4)

Work done in a coil

$W = m B (\cos θ_{1} - \cos θ_{2})$

When it is rotated by angle $180 °$ , then

$W = 2 m B = 2 (N I A) B$ ...(i)

Given, $N = 250, I = 85 μ A = 85 \times 10^{- 6} A$

$A = 1.25 \times 2.1 \times 10^{- 4} m^{2} \approx 2.6 \times 10^{- 4} m^{2}$

$B = 0.85$ $T$

Putting these values in eqn. (i), we get

$W = 2 \times 250 \times 85 \times 10^{- 6} \times 2.6 \times 10^{- 4} \times 0.85$

$\approx 9.1 \times 10^{- 6} J = 9.1$ $μ J$

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