Question 14

A conducting loop of radius $$\frac{10}{\sqrt{\pi}}$$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:

Given: $$r = \frac{10}{\sqrt{\pi}}$$ cm, $$B_0 = 0.5$$ T decreased to 0 in 0.5 s steadily.

Area: $$A = \pi r^2 = \pi \times \frac{100}{\pi} = 100$$ cm² $$= 10^{-2}$$ m²

Rate of change: $$\frac{dB}{dt} = \frac{0.5}{0.5} = 1$$ T/s (constant)

EMF: $$\varepsilon = A \times \frac{dB}{dt} = 10^{-2} \times 1 = 0.01$$ V $$= 10$$ mV

Since the rate is steady, EMF is 10 mV at all times including 0.25 s.

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