A long solenoid of radius 4 cm, length 400 cmcarries a current of 3 A. The total number of turns is 100. Assuming ideal solenoid, find the flux passing through a circular surface having centre on axis of solenoid of radius 3 cm and is perpendicular to the axis of solenoid (i) inside and (ii) at the end of solenoid.

Explanation

Number of turns per unit length is given by
`n=(N)/(l)=(100)/(4)=25"turns/m"`
(i) Magnetic field of a solenoid at a point inside is
`B=mu_(0)ni,S=pir_(1)^(2)andtheta=0^(@)`
Magnetic flux
`phi_(B)=BScostheta=mu_(0)nipir_(1)^(2)cos0^(@)`
`=4pixx10^(-7)xx25xx3xxpixx(3xx10^(-2))^(2)`
`=0.27xx10^(-6)Wb=0.27muWb`
(ii) At the end, magnetic field of solenoid is given by
`=(1)/(2)mu_(0)ni`.
`because" "phi=(0.27)/(2)=0.135muWb`