A square loop of side 0.50 m is placed in a uniform magnetic field ...

Question

A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60 in 0.2 s. The value of emf induced in the loop will be :

Accepted Answer

Side $=0.5$ m, $A=0.25	ext{ m}^2$, $B=0.4$ T (initially perpendicular to loop). Initial flux: $\Phi_i=BA\cos0°=0.4	imes0.25=0.1$ Wb After rotating $60°$: $\Phi_f=BA\cos60°=0.4	imes0.25	imes0.5=0.05$ Wb $$\Delta\Phi=0.1-0.05=0.05	ext{ Wb}$$ $$\varepsilon=\frac{\Delta\Phi}{\Delta t}=\frac{0.05}{0.2}=0.25	ext{ V}$$ (Note: this computed value doesn't exactly match any of the listed options, possibly due to numeric values being altered during text extraction from the source PDF — please cross-check the given B, side length, angle, and time against the original paper.)

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