Electro Magnetic Induction And Alternating Currents Question 345
Question: What is the mutual inductance of a two-loop system as shown with centre separation l
Options:
A) $ \frac{{\mu_{0}}\pi a^{4}}{8l^{3}} $
B) $ \frac{{\mu_{0}}\pi a^{4}}{4l^{3}} $
C) $ \frac{{\mu_{0}}\pi a^{4}}{6l^{3}} $
D) $ \frac{{\mu_{0}}\pi a^{4}}{2l^{3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
Magnetic field at the location of coil (2) produced due to coil (1) $ B_{1}=\frac{{\mu_{o}}}{4\pi }.\frac{2M}{l^{3}} $ Flux linked with coil (2)
$ {\varphi_{2}}=B_{1}A_{2}=\frac{{\mu_{o}}}{4\pi }\frac{2i\ (\pi a^{2})}{l^{3}}\times (\pi a^{2}) $
Also $ {\varphi_{2}}=Mi $
$ \Rightarrow M=\frac{{\mu_{o}}\pi a^{4}}{2l^{3}} $
