First slide

Torque on a current carrying loop placed in uniform magnetic field

Question

A square loop having length of side 1 m is liying in the xy plane. A uniform magnetic field $\vec{B} = (2 \hat{i} - 3 \hat{j} + \hat{k}) T$ exists in that region of space. If the loop carries a current of 2A, the magnitude of torque experienced by the loop is,

Difficult

A

$\sqrt{4} N - m$
B

$7 N - m$
C

$\sqrt{52} N - m$
D

$8 N - m$

Solution

magnetic dipole moment of the loop $\vec{M} = 2 \times {(1)}^{2} \hat{k} N - m = 2 \hat{k} N - m$
$∴ \vec{τ} = \vec{M} \times \vec{B} = 2 \hat{k} \times (2 \hat{i} - 3 \hat{j} + \hat{k}) N - m = (4 \hat{j} + 6 \hat{i}) N - m$
$∴ |\vec{τ}| = \sqrt{4^{2} + 6^{2}} N - m = \sqrt{52} N - m$

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