CUET · PHYSICS · PYQ PAPER 2023
A short solenoid of radius a and \( n_{1} \) number of turns per unit length and length L is kept coaxially inside a very long solenoid of radius b and \( n_{2} \) number of turns per unit length. What is the mutual inductance of the system.
- A \( \mu_{0} \pi b^{2} n_{1} n_{2} L \)
- B \( \mu_{0} \pi a^{2} n_{1} n_{2} L^{2} \)
- C \( \mu_{0} \pi a^{2} n_{1} n_{2} L \)
- D \( \mu_{0} \pi b^{2} n_{1} n_{2} L^{2} \)
Answer & Solution
Correct Answer
(C) \( \mu_{0} \pi a^{2} n_{1} n_{2} L \)
Step-by-step Solution
Detailed explanation
\(B = \mu_0 n_2 I\) \(\Phi = N_1 B A_1 = (n_1 L) (\mu_0 n_2 I) (\pi a^2)\) \(M = \frac{\Phi}{I} = \frac{(n_1 L) (\mu_0 n_2 I) (\pi a^2)}{I}\) \(M = \mu_0 n_1 n_2 \pi a^2 L\)
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