A small square loop of wire of side l is placed inside a large square loop of wire of side L L = l 2 . The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is x × 10 - 7 H , where x = ______.

Step-by-step solution

Flux linkage for inner loop ϕ = B center × l 2 = 4 × μ 0 i 4 π L 2 sin 45 ° + sin 45 ° l 2 ⇒ ϕ = 2 2 μ 0 i π L l 2 Therefore, mutual inductance will be M = ϕ i = 2 2 μ 0 l 2 π L = 2 2 μ 0 π = 2 2 4 π π × 10 - 7 = 8 2 × 10 - 7 = 128 × 10 - 7 H Hence, x = 128 .