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 `(1.0 xx 10^-2)` T near the centre of the solenoid.

Explanation

Given `(R )/(l) = 0.01 Omega`
radius r = 1.0cm`
`n=400, B = 1.0xx10^(-2) T`
:. `I =(E )/(R _o) = (E )/(0.01xx2pixx400)`
`= (E)/(0.01xx2 pixx0.01xx400)
We know that `B = mu_oni`
`1xx10^(-2) = 4pixx 10^(-7)xx`
`(400)/(20xx10^(-2) xx (E )/(2pixx4xx10^(-2)`
`E = (10^(-2)xx20xx10^(-2)xx2xx10^(-2))/(10^(-7)xx4xx10^2`
=1V.