MHT CET · Physics · Electromagnetic Induction
To manufacture a solenoid of length ' \(\ell\) ' and inductance ' \(L\) ', the length of the thin wire required is (Diameter of the solenoid is very less than length, \(\mu_0=\) permeability of free space)
- A \(\left[\frac{4 \pi \ell \mathrm{~L}}{\mu_0}\right]^{\frac{1}{2}}\)
- B \(\left[\frac{2 \pi \ell}{\mu_0 L}\right]^{\frac{1}{2}}\)
- C \(\left[\frac{4 \pi \mu_0}{\ell \mathrm{~L}}\right]^{\frac{1}{2}}\)
- D \(\left[\frac{2 \pi \mu_0 \mathrm{~L}}{\ell}\right]^{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(A) \(\left[\frac{4 \pi \ell \mathrm{~L}}{\mu_0}\right]^{\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
\(L = \frac{\mu_0 N^2 (\pi r^2)}{\ell}\) \(N r = \sqrt{\frac{L \ell}{\mu_0 \pi}}\)
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