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Q charge is uniformaly distributed over the same surface of a right circular cone of semi -vertical angle theta and height h The cone is uniformly rotated about its axis at angular velocity omega Calculated associated magnetic dipole moment
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Text Solution

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A ring of radius `r` with charge `q` rotating with angular velocity `omega` is equilvant to a dipole of dipole moment
`=NIA=qfA=q(omega)/(2pi)A`
dipole moment of differential ring
`dp=(Q)/(piRl)2pir(dx)/(costheta)*(omega)/(2pi)pir^(2)`
`(R )/(r )=(h)/(h-x)`
`rArr dp=(Qcostheta)/(piR.h)(dx)/(costheta)omegapi((h-x)/(n)R)^(3)`
`rArr P=(Qomega.R^(2))/(h^(4))int_(0)^(h)(h-x)^(3)dx=(QomegaR^(2))/(h^(4))*|((h-x)^(4))/(4)|_(h)^(0)`
`=(omegaQR^(2))/(h^(4))(h^(4))/(4)=(QomegaR^(2))/(4)=(Qomega)/(4)h^(2)tan^(2)theta`
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