A small square loop of wire of side l is placed inside a large square loop of wire of side LL=l^2. The loops are coplanar and their centers coincide…

Question

A small square loop of wire of side l is placed inside a large square loop of wire of side LL=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=______.

MARKS Content Team · Accepted Answer

Correct answer: 128. Flux linkage for inner loop ϕ=B_center×l^2 =4×(μ_0i)/(4πL2)sin45°+sin45°l^2 ⇒ϕ=2√2(μ_0i)/(πL)l^2 Therefore, mutual inductance will be M=(ϕ)/i=(2√2μ_0l^2)/(πL)=2√2μ_0π =2√2(4π)/(π)×10^(-7) =8√2×10^(-7) =√128×10^(-7) H Hence, x=128.

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 $\sqrt{x} \times 10^{- 7} H$ , where $x =$ ______.

Solution

Relevant Questions

A small square loop of wire of side l is placed inside a large square loop of wire of side LL=l2. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is x×10-7 H, where x=______.

Solution

Relevant Questions

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 $\sqrt{x} \times 10^{- 7} H$ , where $x =$ ______.