Question

The magnetic field at distance y from the centre on the axis of a disk of radius r and uniform surface charge density σ spinning with angular velocity ω is?​

Answer 1

Answer:

B=2μ0σω/2(r²+y2y²/sq.root of (r²+y²)−2y).

Explanation:

Charge on a ring of radius x and width dx 

dq=2(πxdx)σ

Current, dl=dq/dt=dt=2πxσdx/dt=ωσxdx

dBl=2μ0dlr²/2(x²+y²)³/²

B=2μ0σω/2(r²+y2y²/sq.root of (r²+y²)−2y).

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Answer 2

Charge on a ring of radius x and width dx

dq=2(πxdx)σCurrent, dl= dt dq = dt2πxσdx =ωσxdxdB= 2(x 2 +y 2 )

3/2μ0 dlr 2B= 2μ 0 σω

( r 2 +y 2r 2 +2y 2 −2y).