Electro Magnetic Induction And Alternating Currents Question 494
Question: A wire of fixed lengths is wound on a solenoid of length $ \ell $ and radius r. Its self-inductance is found to be L. Now if same wire is wound on a solenoid of length $ \ell /2 $ and radius r/2, then the self in- ductance will be -
Options:
A) 2L
B) L
C) 4L
D) 8L
Show Answer
Answer:
Correct Answer: A
Solution:
-
$ L=\frac{{\mu_{0}}N^{2}\pi r^{2}}{\ell } $ Length of wire=N
$ 2\pi r $ =constant (=C, suppose)
$ \therefore L={\mu_{0}}{{( \frac{C}{2\pi r} )}^{2}}\frac{\pi r^{2}}{\ell } $
$ \therefore L\propto \frac{1}{\ell } $
$ \therefore $ Self-inductance will become 2L.
