A 10 m long horizontal wire extends from North East to South West.
Question:

A $10 \mathrm{~m}$ long horizontal wire extends from North East to South West. It is falling with a speed of $5.0 \mathrm{~ms}^{-1}$, at right angles to the horizontal component of the earth’s magnetic field, of $0.3 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^{2}$. The value of the induced emf in wire is :

1. (1) $1.5 \times 10^{-3} \mathrm{~V}$

2. (2) $1.1 \times 10^{-3} \mathrm{~V}$

3. (3) $2.5 \times 10^{-3} \mathrm{~V}$

4. (4) $0.3 \times 10^{-3} \mathrm{~V}$

Correct Option: 1

Solution:

(1) Induced emf, $\varepsilon=\mathrm{B} v \ell$

$=0.3 \times 10^{-4} \times 5 \times 10$

$=1.5 \times 10^{-3} \mathrm{~V}$