Question

The length of a thin wire require to manufacture a solenoid of length $l=100$ cm and inductance $L=1mH$, if the solenoid's cross-sectional diameter is considerably less than its length is:

• A. $1km$
• B. $0.10km$
• C. $0.010km$
• D. $10km$

Answer 1

The correct option is B $0.10km$

Let $l_1$ is the length of wire,
$l_1=2\pi rN\Rightarrow Nr=\frac{l_1}{2\pi }\Rightarrow L=\frac{{\mu }_0\pi r^2{N}^2}{l}=\frac{{\mu }_0\pi }{l}\frac{l_1^2}{4{\pi }^2}$
$\Rightarrow l_1=\sqrt{\frac{Ll4\pi }{{\mu }_0}}=\sqrt{\frac{{10}^{-3}\times 1\times 4\pi }{4\pi \times {10}^{-7}}}={10}^{2}m=0.10km$