Electro Magnetic Induction And Alternating Currents Question 316
Question: A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to [IIT JEE 1998]
Options:
A) l / L
B) $ l^{2}/L $
C) $ L/l $
D) $ L^{2}/l $
Show Answer
Answer:
Correct Answer: B
Solution:
Magnetic field produced due to large loop
$ B=\frac{{\mu_{0}}}{4\pi }\frac{8\sqrt{2}i}{L} $ Flux linked with smaller loop
$ \varphi =B(l^{2})=\frac{{\mu_{0}}}{4\pi }\frac{8\pi il^{2}}{L} $
$ \therefore \varphi =Mi\Rightarrow M=\frac{\varphi }{i}=\frac{{\mu_{0}}}{4\pi }.\frac{8\sqrt{2}l^{2}}{L}\Rightarrow M\propto \frac{l^{2}}{L} $
