Question

A rectangular coil of $300$ turns has an average area of $25cm\times 10cm$. The coil rotates with a speed of $50cps$ in uniform magnetic field of strength $4\times {10}^{-2}T$ about an axis perpendicular to the field. The peak value of the induced emf is (in volt):

• A. $300\pi$
• B. $3000\pi$
• C. $3\pi$
• D. $30\pi$

Answer 1

Answer: (C)

$3\pi$

Peak voltage will be induced when the longer side moves perpendicular to the magnetic field in which case the axis will be parallel to the longer end.

$\omega =2\pi f=2\pi \left(50\right)=100\pi$

Area $=A=250c{m}^2=250\times {10}^{-4}{m}^2$

Peak induced voltage will be:

$V=NAB\omega$

$⟹300\times 250\times {10}^{-4}\times 4\times {10}^{-2}\times 100\pi$

$=3\pi volt$