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.



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