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Calculate the magnetic field at distance...

Calculate the magnetic field at distance `y` from the centre of the axis of a disc of radius `r` and unifrom surface charge density `sigma`, If the disc spins with angular velocity `omega` ?

A

`(mu_(0)sigmaomega)/(3)((r^(2)-2y^(2))/(sqrt(r^(2)-y^(2)))+2y)`

B

`(mu_(0)sigmaomega)/(2)((r^(2)+2y^(2))/(sqrt(r^(2)+y^(2))))`

C

`(mu_(0)sigmaomega)/(2)((r^(2)+2y^(2))/(sqrt(r^(2)+y^(2)))-2y)`

D

`(2mu_(0)sigmaomega)/(3)((r^(2)+2y^(2))/(sqrt(r^(2)+y^(2)))-2y)`

Text Solution

Verified by Experts

Charge on a ring of radius `x` and width `dx`
`dq=(2pix dx)sigma`
Current, `dI=(dq)/(dt)=(2pixsigmadx)/(Dt)=omegasigmax dx`
`dB=(mu_(0)dIr^(2))/(2(x^(2)+y^(2))^(3//2))`
`B=(mu_(0)sigmaomega)/(2)((r^(2)+2y^(2))/(sqrt(r^(2)+y^(2)))-2y)`
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