The magnetic field B crossing normally a square metallic plate of area $4 \mathrm{~m}^{2}$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $t=2 \mathrm{~s}$ to $t=4 \mathrm{~s}$, is ______ mV

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Electromagnetic Induction

The magnetic field B crossing normally a square metallic plate of area

4 m^{2}

is changing with time as shown in figure. The magnitude of induced emf in the plate during

t = 2 s

t = 4 s

, is ______ mV

Answer: 8

Solution

The field grows linearly with slope

\frac{d B}{d t} = \frac{10 - 0}{5 - 0} = 2

mT/s

= 2 \times 1 0^{- 3}

T/s, and this slope holds throughout the interval from

2

s to

4

s. By Faraday's law the induced emf is

ε = A \frac{d B}{d t} = (4) (2 \times 1 0^{- 3}) = 8 \times 1 0^{- 3}

V. The magnitude of the induced emf is

8

mV.

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Integer answer

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