Two concentric circular coils, C 1 and C 2 , are placed in the X Y plane. C 1 has 500 turns, and a radius of 1 cm . C 2 has 200 turns and radius of 20 cm . C 2 carries a time dependent current I t = 5 t 2 - 2 t + 3 A where t is in s. The emf induced in C 1 in mV at the instant t = 1 s is 4 x . The value of x is ..........

Step-by-step solution

I = 5 t 2 + 2 t + C d i d t = ( 10 t + 2 ) ϕ small  = B A = μ 0 I N 2 2 R π r 2 induced emf in small coil e = d ϕ dt = μ 0 N 2 2 r π r 2 N 1 di dt = μ 0 N 1 N 2 π r 2 2 R ( 10 t - 2 ) at t = 1 e = μ 0 N 1 N 2 π r 2 2 R 8 = 4 μ 0 N 1 N 2 π r 2 R = 4 ( 4 π ) 10 - 7 × 200 20 × 500 × 10 - 4 10 - 2 π = 80 × π 2 × 10 - 7 × 10 × 10 2 × 10 - 2 = 8 × 10 - 4   volt = 0 . 8   mV = 4 x x = 5