A circular coil has 100 turns, radius 3 cm and resistance 4 Ω . This coil is co-axial with a solenoid of 200 turns/cm and diameter 4 cm . If the solenoid current is decreased from 2 A to zero in 0 . 04 s , then the current induced in the coil is

Step-by-step solution

Magnetic field due to a solenoid is given by, B = μ 0 n i . Therefore, flux through the coil will be, ϕ = B A = μ 0 n i N π r 2 . According to Faraday's law of electromagnetic induction ε = ∆ ϕ ∆ t . Therefore, i = ∆ ϕ R ∆ t = μ 0 n N π r 2 R × ∆ i ∆ t = 4 π × 10 - 7 × 200 × 100 × π × 0 . 03 2 4 × 2 0 . 04 ⇒ i = 9 π 2   mA