Question

A small square loop of wire of side l is placed inside a large square loop of wire L(L>>l). As shown in figure, both loops are coplanar and their centers coincide at point O. The mutual inductance of the system is:

• A. \(\frac{2\sqrt2 \mu_0L^2}{\pi l}\)
• B. \(\frac{\mu_0L^2}{2\sqrt2 \pi L}\)
• C. \(\frac{2\sqrt 2 \mu_0 l^2}{\pi L}\)
• D. \(\frac{\mu_0L^2}{2\sqrt2\pi l}\)

Answer 1

The Correct Option is C

B₁=4B=\(\frac{4μ_0i}{4π(\frac{L}{2})(2sin45°)}\)
B1=\(\frac{2\sqrt 2 \mu_0 l^2}{\pi L}\)
M=\(\frac{Flux inner loop}{i}\)=\(\frac{2\sqrt 2 \mu_0 il^2}{i\pi ^2}\)
=\(\frac{2\sqrt2 \mu_0l^2}{\pi L}\)