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A long solenoid of radius 4 cm, length 4...

A long solenoid of radius 4 cm, length 400 cm carries a current of 3A. 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 3cm and is perpendicular to the axis of solenoid in side.

Text Solution

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Given : Number of turns per unit length, `n=(N)/(l)`
`n=(100)/(4)=25"turns"//m`
Formula :
Magnetic field of a solenoid at a point inside is `B=mu_(0)ni`
Area of cross section of the solenoid,
`A=pi_(1)^(2)andtheta=0^(@)`
Magnetic flux, `phi_(B)=BAcostheta`
`=(muni)(pir^(2))cos0^(@)(theta=0^(@))`
`4pixx10^(-7)xx25xx3xxpi(3xx10^(-2))^(2)`
`phi_(B)=0.27xx10^(-6)Wb`
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