Question

A coil of 20 $\times$ 20 cm having 30 turns is making 30 rps in a magnetic field of induction 1 tesla. The peak value of the induced e.m.f. is approximately
A. 452 volts
B. 226 volts
C. 113 volts
D. 339 volts

Answer 1

Hint: Use concepts of topic Electromagnetic Induction & Alternating Current. Use $\omega = 2\pi v$ where $v$ = frequency. Electromagnetic Induction states that the emf induced in a loop due by a changing magnetic flux is equal to the rate of change of the magnetic flux threading the loop.

Formula: Rate of change of flux = $e.m.f. = NBA\omega $

Complete step by step solution:
 Given,
$v = 30rps,N = 30,A = (20 \times 20)c{m^2} = 400c{m^2} = 0.04{m^2},B = 1T$
v =frequency
N = no. of turns
A= Area
B=magnetic field
Using formula, $e.m.f. = NBA\omega $
peak value of the induced e.m.f. = $NBA\omega = NBA\left( {2\pi v} \right) = 30 \times 1 \times 0.04 \times \left( {2\pi \times 30} \right) = 226V$

Correct Answer: B) 226 volts

Note: When a conductor is moved through a magnetic field, an EMF is generated and the interaction of the magnetic field produced by the conductor with the magnetic field that was present causes deflection.