A circular loop of radius R carrying current I is kept in XZ plane. A uniform and constant magnetic field B → = B 0 i ^ + 2 B 0 j ^ + 3 B 0 k ^ exists in the region ( B 0 - a positive constant) . Then the magnitude of the torque acting on the loop will be

Magnetic dipole moment, M → = ± I π R 2 j ^ τ → = M → × B → = ± I π R 2 j ^ × B 0 i ^ + 2 B 0 j ^ + 3 B 0 k ^ τ → = ± I π R 2 B 0 - k ^ + 3 i ^

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Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismMagnetic torque & energyMedium2 minPYQ_2020

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A circular loop of radius $R$ carrying current $I$ is kept in $XZ$ plane. A uniform and constant magnetic field $\vec{B} = (B_{0} \hat{i} + 2 B_{0} \hat{j} + 3 B_{0} \hat{k})$ exists in the region ( $B_{0}$ - a positive constant) . Then the magnitude of the torque acting on the loop will be

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Answer:

Solution:

Magnetic dipole moment, $\vec{M} = \pm I π R^{2} \hat{j}$

$\vec{τ} = \vec{M} \times \vec{B} = \pm I π R^{2} \hat{j} \times (B_{0} \hat{i} + 2 B_{0} \hat{j} + 3 B_{0} \hat{k})$

$\vec{τ} = \pm I π R^{2} B_{0} [- \hat{k} + 3 \hat{i}]$

Stream:JEESubject:PhysicsTopic:MagnetismSubtopic:Magnetic torque & energy

⏱ 2mℹ️ Source: PYQ_2020

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