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 emf induced in coil will be

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 emf induced in coil will be (A) 1.158 V (B) 0.58 V (C) 0.29 V (D) 5.8 V

Tardigrade Admin · Accepted Answer

Here: n=4000, B=0.5 × 10-4 Wb / m 2 Rate of rotation of coil =1800 rev / min =(1800/60)=30 rev / sec ω=2 π f=2 π × 30=60 π rad / s r=7 cm =0.07 m Now area of coil A=π r2=π ×(0.07)2=49 π × 10-4 m 2 Now the maximum energy induced is e =B A n ω =0.5 × 10-4 × 49 π × 10-4 × 4000 × 60 π =0.58 V

Q. A circular coil of mean radius of 7cm 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 emf induced in coil will be

1.158 V

0.58 V

0.29 V

5.8 V

Here: n=4000,B=0.5×10−4Wb/m2 Rate of rotation of coil =1800rev/min =601800​=30rev/sec ω=2πf=2π×30=60πrad/s r=7cm=0.07m Now area of coil A=πr2=π×(0.07)2=49π×10−4m2 Now the maximum energy induced is e=BAnω =0.5×10−4×49π×10−4×4000×60π =0.58V

Q. A circular coil of mean radius of $7 c m$ 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 emf induced in coil will be