Electromagnetic Induction And Alternating Current Ques 38

Answer:

Correct Answer: 38.(a)

Solution:

Formula:

# Self induction:

38. (a) Self inductance $L _{sol}$ of a solenoid is given by

$$ L _{sol}=\mu _0 n^{2} \pi r^{2} L $$

(Here, $n=N / L$ and $L=$ length of solenoid)

$$ \begin{array}{ll} \text { or } & L _{sol}=\frac{\mu _0 N^{2} \pi r^{2}}{L} \\ \text { Clearly, } & L _{sol} \propto \frac{1}{L} \end{array} $$

( $\because$ All other parameters are fixed)

NOTE We can determine expression of $L$ as follows

$$ \varphi=N B A=L _{\text {sol }} l $$

But for a solenoid, $B=\mu _0 n l, A=\pi^{2}$

$$ \begin{array}{ll} \therefore & L _{\text {sol }} l=\mu _0 n / \pi^{2} N \\ \text { or } & L _{\text {sol }}=\mu _0 n^{2} \pi^{2} L=\mu _0 \frac{N^{2}}{L} \pi r^{2} \end{array} $$