Question

A semicircular wire of radius $0.5\text{m}$ is rotating in the magnetic field of magnitude $10\text{T}$ as shown in the figure. If the angular velocity of the wire is $12\text{rad/s},$ calculate the emf generated across the ends of the wire.

Answer 1

Emf across an irregular shaped wire can be calculated by replacing the irregular shaped wire with an imaginary wire formed by joining the ends of the irregular wire.


$\therefore$ The effective length of the wire is,

$l=2r=2\times 0.5=1\text{m}$

$\therefore$ Emf induced across the ends of the wire is,

$E=\frac{B\omega l^2}{2}=\frac{10\times 12\times 1^2}{2}=60\text{V}$

Correct answer: $60$

Why this question : This question gives you an idea of how to calculate emf across an irregular shaped wire rotating in a magnetic field.