Two concentric circular coils with radii 1 cm and 1000 cm and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____ × 10 – 8 H . (Take, π 2 = 10 )

Step-by-step solution

Let the magnetic field of the 200 turns be B 1 . The formula of magnetic field is given by B = μ 0 i 2 r Let r = 1000   cm . Thus, B 1 = n μ 0 × I 2 × 10 = 200 μ 0 I 2 × 10 The flux through the coil of radius r 1 = 1   cm is ϕ = 10 × B → · A → = 10 × B 1 π r 2 1 ⇒ ϕ = 10 × 200 μ 0 I 2 × 10 × π 0 . 01 2 L = 10 × 200 μ 0 2 × 10 × π 0 . 01 2 = 10 × 200 4 π × 10 - 7 2