A constant magnetic field of 1 T is applied in the $\mathrm{x}>0$ region. A metallic circular ring of radius 1 m is moving with a constant velocity of $1 \mathrm{~m} / \mathrm{s}$ along the $x$-axis. At $t=0$, the centre of $O$ 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.)

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Electromagnetic Induction

A constant magnetic field of 1 T is applied in the

x > 0

region. A metallic circular ring of radius 1 m is moving with a constant velocity of

1 m / s

along the

x

-axis. At

t = 0

, the centre of

O

of the ring is at

x = - 1 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.)

Answer: (C)

t = 0

, center is at

x = - 1

m. At

t = 1

s, center is at

x = - 1 + 1 (1) = 0

m. The ring is entering the magnetic field region (

x > 0

). The rate of change of flux is

\frac{d Φ}{d t} = B \cdot \frac{d A}{d t}

. The area entering per unit time is the area swept by the diameter:

\frac{d A}{d t} = 2 r \cdot v = 2 (1) (1) = 2

m²/s. Therefore, induced emf

= B \frac{d A}{d t} = 1 \times 2 = 2

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Single correct option