Physics - Magnetism Question with Solution | TestHub

Due to z component of field loop experiences force in x-y plane which do not gives any torque about axis. Due to x-component there is no force on PQ and RS branch of loop. Force on QR and SP branch are 2iBa (inwards) and iBa (outwards) respectively.

Torque on loop due to these forces

$$\left(-\frac{\mathrm{a}}{2\sqrt{2}}\mathrm{i}\mathrm{Ba}+\frac{3\mathrm{a}}{2\sqrt{2}}2\mathrm{iBa}\right)={\mathrm{iBa}}^2\left[\frac{5}{2\sqrt{2}}\right]$$

moment of inertia of loop about given axis

$$=\frac{\mathrm{m}(\mathrm{a}\sqrt{2}{)}^2}{3}=\frac{2}{3}{\mathrm{ma}}^2$$

instantaneous angular acceleration of loop

$$\alpha =\frac{\tau }{\mathrm{I}}=\frac{15\mathrm{iB}}{4\sqrt{2}\mathrm{m}}.$$