A long solenoid of radius `3cm` , length `I00cm` carries a current of `4A` . The total number of truns is `300` . Assuming ideal solenoid, find the flux passing through a circular surface having centre on axis of solenoid,
(a) of radius `2cm` and is perprndicular of the axis of solenoid (i) inside and (ii) at the end of solenoid
(b) of radius `4cm` and is perprndicular of the axis of solenoid
(c) of radius greater than `3cm` and angle between normal to area and axis of solenoid is `60^(@)C`

Explanation

`n=(N)/(l)=(300)/(I)=300turns//m`
(a) `B=mu_(0)ni` , `A=pir_(I)^(2)` , `theta=0^(@)`
`phi=Bacostheta=mu_(0)ni.pir_(I)^(2)cos0`
`=4pixxI0^(-7)xx300xx4xxpixx(2xxI0^(-2))^(2)`
`=I.92xxI0^(-6)` where `=I.92muWb`
At the end : `B : (I)/(2)mu_(0)ni`
`pi=(I.92)/(2)=0.92muWb`
(b) The magnetic field exists only in radius `3cm`
`Apir^(2)`
`phi=(I.92xxpi(3)^(2))/(pi(2)^(2))=4.32muWb`
(c) `theta=60^(@)` , `phi=4.32cos60^(@)=2.I6Wb`
`theta=90^(@)` , `phi=0`