JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Electromagnetic Induction

A conducting loop of radius

\frac{10}{π} 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:

(A) $emf = 1 mV$
(B) $emf = 10 mV$ ✓ Correct
(C) $emf = 100 mV$
(D) $emf = 5 mV$

Answer: (B)

Solution

The flux through the loop is

ϕ = B A

, and because the field falls at a steady rate the induced emf

\frac{A Δ B}{Δ t}

is the same at every instant, the moment

0.25 s

included. The area is

A = π r^{2} = π (\frac{0.1}{π})^{2} = 0.01 m^{2}

. With the field dropping by

0.5 T

over

0.5 s

, the induced emf is

\frac{0.01 \times 0.5}{0.5} = 0.01 V = 10 mV

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Single correct option

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