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A constant magnetic field of $1 \mathrm{~T}$ is applied in the $x>0$ region. A metallic circular ring of radius $1 \mathrm{~m}$ is moving with a constant velocity of $1 \mathrm{~m} / \mathrm{s}$ along the $x-axis$ , At $t=0 \mathrm{~s}$ , the centre $\mathrm{O}$ of the ring is at $x=-1 \mathrm{~m}.$ What will be the value of the induced emf in the ring at $t=1 s$ ? (Assume the velocity of the ring does not change.)
Option: 1 $2\pi V$
Option: 2 $2V$
Option: 3 $0V$
Option: 4 $1V$

Answers (1)

best_answer

At t = 0

At t=1s,

$dA= \left ( 2R \right )dx\\$

$e= \left | \frac{d\phi}{dt} \right |= \left | \frac{d\left ( BA \right )}{dt} \right |\\$

$= B\left | \frac{dA}{dt} \right |= B\times 2R\left | \frac{dx}{dt} \right |\\$

$= 1\times(2)\times1\\$

$e= 2V$

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