Question

In a region of uniform magnetic induction B= 10⁻² tesla , a circular coil of radius 30 cm and resistance π² ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is(a) 4π² mA(b) 30 mA(c) 6 mA(d) 200 mA

Answer 1

Correct Answer is option (c) 6 mA

Given :  

                 

B = 10⁻² T

Coil radius = R = 30 cm = 0.3 m

  R = π² Ω

ω = 200 rpm

hence ω = 2π × (200 / 60) rad/sec

E = NBAW sin ωt

Eo = NBAW    

Io = (Eo / R)

= [{NBAW} / R]

= = [{1 × 10⁻² × πR² × 2π × (200 / 60)} / {π²}]

= R² × 10⁻²× 2 × (10 / 3)

= (2R² / 3) × 10⁻¹

= [{2 × (0.3)²} / {3}] × 10⁻¹

=6 × 10⁻³A

= 6 mA.

∴the amplitude of the alternating current induced in the coil is 6mA

                             

                 

               

                 

                                   

Answer 2

Option C is correct.

6 mA.