A) \[\sqrt{\frac{2\pi L{{l}_{0}}}{{{\mu }_{0}}}}\]
B) \[\sqrt{\frac{4\pi L{{l}_{0}}}{\mu _{0}^{2}}}\]
C) \[\sqrt{\frac{4\pi L{{l}_{0}}}{{{\mu }_{0}}}}\]
D) \[\sqrt{\frac{8\pi L{{l}_{0}}}{{{\mu }_{0}}}}\]
Correct Answer: C
Solution :
Suppose solenoid has N turns, each of radius r and length of wire is l. It?s self inductance \[L=\frac{{{\mu }_{0}}{{N}^{2}}A}{{{l}_{0}}}=\frac{{{\mu }_{0}}{{N}^{2}}\pi {{r}^{2}}}{{{l}_{0}}}\] .... (i) Also length of the wire \[l=N\times 2\pi r\] \[\Rightarrow {{N}^{2}}{{r}^{2}}=\frac{{{l}^{2}}}{4{{\pi }^{2}}}\] .... (ii) From equation (i) and (ii) \[l=\sqrt{\frac{4\pi L{{l}_{o}}}{{{\mu }_{o}}}}\]You need to login to perform this action.
You will be redirected in
3 sec