If the self inductance of 500 turn coil is 125 mH then the self inductance of similar coil of 800 tu

Question

If the self inductance of 500 turn coil is 125 mH then the self inductance of similar coil of 800 turns is\

Professor PC Thomas Classes · Answer

D) Self inductance of a coil, $\mathrm{L}=\mu, \mu_{0} \mathrm{n}^{2} \mathrm{~A} \ell$ where $\mu_{\mathrm{r}}$ is the relative permittivity of the core, n is the number of turns per unit length, A , the area of cross-section, $l$, the length of the solenoid $\mathrm{L} \propto \mathrm{n}^{2}$\ Self inductance of 500 turns coil $=124 \mathrm{mH}$\ $	herefore \mathrm{L}$ for the coil of 800 turns $=\frac{(125)}{(500)^{2}} 	imes 800^{2}$\ $\mathrm{L}=320 \mathrm{mH}$\