Question

A circular coil of mean radius of 7 cm and having 4000 turns is rotated at the rate of 1800 revolutions per minute in the earth's magnetic field (B = 0.5 gauss), the maximum e.m.f. induced in coil will be(a) 1.158 V(b) 0.58 V(c) 0.29 V(d) 5.8 V

Answer 1

Correct Answer is option B : 0.58V

explanation :

r= 7cm= 7 x 10⁻² m

n=400 turns

revolutions= ω=1800 revolution/min=1800/60 revolution/sec

B= 0.5 guass= 0.5 x 10⁻⁴ T

e₀=ωNBA

=(2πν)NB(πr²)=2×π²ν NBr²

=2×(3.14)²×[1800/60]×4000×0.5×10⁻⁴×(7×10⁻²)²  

=0.58 V