CBSE 2026 · Region 5 · Set 1 · Q32 · 5 marks

(a)OR(b)

(i)

A rectangular loop of sides a and b carrying current I is placed in a magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$ such that its area vector $\displaystyle \overrightarrow{\mathrm{A}}$ makes an angle $\displaystyle \theta$ with $\displaystyle \overrightarrow{\mathrm{B}}$. With the help of a suitable diagram, show that the torque $\displaystyle \vec{\tau}$ acting on the loop is given by $\displaystyle \vec{\tau}=\vec{\mathrm{m}} \times \vec{\mathrm{B}}$, where $\displaystyle \vec{\mathrm{m}}(=\mathrm{I} \vec{\mathrm{A}})$ is the magnetic dipole moment of the loop.

(ii)

A circular coil of $\displaystyle 100$ turns and radius $\displaystyle \left(\frac{10}{\sqrt{\pi}}\right) \mathrm{cm}$ carrying current of $\displaystyle 5 \cdot 0 \mathrm{~A}$ is suspended vertically in a uniform horizontal magnetic field of $\displaystyle 2.0$ T. The field makes an angle $\displaystyle 30$° with the normal to the coil. Calculate :

(I)

the magnetic dipole moment of the coil, and

(II)

the magnitude of the counter torque that must be applied to prevent the coil from turning.

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CBSE Class 12 Physics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.