Question

A copper wire having resistance 0.01 ohm in each metre is used to wind a 400-turn solenoid of radius 1.0 cm and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of 1$1.0\times {10}^{-2}T$ near the centre of the solenoid.

Answer 1

Given $\frac{R}{l}=0.01\Omega ,$

radius $r=1.0cm$

$n=400,B=1.0\times {10}^{-2}T$

$\therefore i=\frac{E}{R_0}=\frac{E}{0.01\times 2\pi r\times 400}$

$=\frac{E}{0.01\times 2\times \pi \times 0.01\times 400}$

We know that

$B={\mu }_{o}ni$

$1\times {10}^{-2}=4\pi \times {10}^{-7}\times \frac{400}{20\times {10}^{-2}}\times \frac{E}{2\pi \times 4\times {10}^{-2}}$

$E=\frac{{10}^{-2}\times 20\times {10}^{-2}\times 2\times {10}^{-2}}{{10}^{-7}\times 4\times {10}^2}$

$=1V.$