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$^{-1}$ along the $x$-axis. At $t = 0$ s, the centre $O$ 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: (B) $2$ V
At $t = 1$ s the centre is at $x = 0$, so the boundary of the field region passes through the centre of the ring.
The emf equals $B\,v\,\ell$, where $\ell$ is the length of the chord along the boundary (the rate at which area enters the field is $\ell v$). Here $\ell$ is the diameter, $2$ m:
$$\varepsilon = 1\times1\times2 = 2\ \text{V}$$
Solution by Sreeraj P, M.Sc Physics