A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of $50 \mathrm{rad} \mathrm{s}^{-1}$ in a uniform horizontal magnetic field of $3.0 \times 10^{-2} \mathrm{~T}$. The maximum emf induced in the coil will be _____ $\times 10^{-2}$ volt (rounded off to the nearest integer).

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Electromagnetic Induction

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of

50 rad s^{- 1}

in a uniform horizontal magnetic field of

3.0 \times 1 0^{- 2} T

. The maximum emf induced in the coil will be _____

\times 1 0^{- 2}

volt (rounded off to the nearest integer).

Answer: 60

Solution

A coil turning in a uniform field has flux

N B A cos ω t

, so the induced emf is

N B A ω sin ω t

and its peak value is

ε_{0} = N B A ω

.
The area is

A = π r^{2} = π (0.08)^{2} = 2.01 \times 1 0^{- 2} m^{2}

, so

ε_{0} = 20 \times (3.0 \times 1 0^{- 2}) \times (2.01 \times 1 0^{- 2}) \times 50 = 0.603 V

Written in the required form this is

60.3 \times 1 0^{- 2}

V, which to the nearest integer gives

60

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Numerical answer

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