Q 12-06-141JEE MainJEE Main 2019 (12 Jan, Shift 2)Medium
A $10$ m long horizontal wire extends from North East to South West. It is falling with a speed of $5.0\ \text{m s}^{-1}$, at right angles to the horizontal component of the earth's magnetic field of $0.3\times10^{-4}\ \text{Wb m}^{-2}$. The value of the induced emf in the wire is:
Answer: (B) $1.1\times10^{-3}$ V
The horizontal field points north. The velocity is vertical, so $\vec{v}\times\vec{B}$ is horizontal and east–west. Only the east–west component of the wire's length counts: $l\sin45^\circ$.
$$\varepsilon = Bvl\sin45^\circ = 0.3\times10^{-4}\times5\times10\times\frac{1}{\sqrt2} \approx 1.1\times10^{-3}\ \text{V}$$
Solution by Sreeraj P, M.Sc Physics