A stiff semi-circular wire of radius R is rotated in a uniform magnetic field B about an axis passing through its ends. If the frequency of rotation of the wire is f, calculate the amplitude of the alternating emf induced in the wire.

^{2}.

Therefore, the rate at which the wire traces out the area is

\(\frac{d A}{d t}\) = frequency or rotation × A = fA

If the angle between the uniform magnetic field \(\vec{B}\) and the rotation axis is θ, the magnitude of the induced emf is

|e|= B\(\frac{d A}{d t}\) cosθ = BfA cosθ = Bf(πR^{2})cosθ

so that the required amplitude is equal to Bf(πR^{2})