First slide

Magnetic Dipole moment

Question

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

Moderate

A

$4.55 μ J$
B

$2.3 μ J$
C

$1.15 μ J$
D

$9.1 μ J$

Solution

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)
$Given: N = 250, I = 85 μ A = 85 \times 10^{- 6} A$
$A = 1.25 \times 2.1 \times 10^{- 4} m^{2} \approx 2.5 \times 10^{- 4} m^{2}$
$B = 0.85 T$
Putting these values in eqn. (i), we get
$W = 2 \times 250 \times 85 \times 10^{- 6} \times 2.5 \times 10^{- 4} \times 0.85$
$\approx 9.1 \times 10^{- 6} J = 9.1 μ J$

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