Question 7: Electromagnetic Induction

Question

A rectangular coil of 250 turns has an average area of $20 \mathrm{~cm} 	imes 15 \mathrm{~cm}$. The coil rotates with a speed of 60 cycles per second in a uniform magnetic field of $2 	imes 10^{-2} \mathrm{~T}$ about an axis perpendicular to the field. The peak value of the induced emf is:

Accepted Answer

LetÃ¢ÂÂs collect the data and apply the standard formula for a rotating coil:
Given
Ã¢ÂÂ¢ Number of turns: $N=250$
Ã¢ÂÂ¢ Coil dimensions: $20	ext{ cm}	imes15	ext{ cm}\implies A=0.20	imes0.15=0.03\ \mathrm m^2$
Ã¢ÂÂ¢ Rotation rate: $f=60$ Hz, so $\omega=2\pi f=120\pi\ \mathrm{rad/s}$
Ã¢ÂÂ¢ Magnetic field: $B=2	imes10^{-2}\ \mathrm T$
The induced emf varies as
$ \mathcal{E}(t)=N\,B\,A\,\omega\;\sin(\omega t) $
so the peak (maximum) emf is
$ \boxed{\mathcal{E}_{\max}=N\,B\,A\,\omega.} $
Substituting in:
$ \mathcal{E}_{\max} =250	imes(2	imes10^{-2})	imes0.03	imes(120\pi) =18\pi\ \mathrm V. $
Answer: $18\pi$ V, i.e. option C.

Answer

$36 \pi$ volt

Answer

$30 \pi$ volt

Answer

$18 \pi$ volt

Answer

$12 \pi$ volt

Electromagnetic Induction

A rectangular coil of 250 turns has an average area of 20 \mathrm{~cm} \times 15 \mathrm{~cm}. The coil rotates with a speed of 60 cycles per second in a uniform magnetic field of 2 \times 10^{-2} \mathrm{~T} about an axis perpendicular to the field. The peak value of the induced emf is:

Choose the correct answer: