A constant magnetic field of 1T is applied in the x > 0 region. A...

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

A constant magnetic field of 1T is applied in the x > 0 region. A metallic circular ring of radius 1m is moving with a

Options

A $0V$
B $2V$
C $2\piV$
D $1V$

Correct answer

B. $2V$

Step-by-step solution

Recall the formula of induced E.M.F. in terms of the length of the rod, and uniform magnetic field, $E = Bvl$ , here in the case of the ring, $l = 2R$ , $⇒ E = Bv2R$ , when half ring enters, $E = 1 \times 1 \times 2 \times 1 = 2V$ .

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