A thin circular disk of radius `R` is uniformly charged with density `sigma gt 0` per unit area.The disk rotates about its axis with a uniform angular speed `omega`.The magnetic moment of the disk is :

Options

A. (a)`2piR^(2)sigma omega`
B. (b)`2 piR^(4)sigma omega`
C. (c)`(piR^(4))/2 sigma omega`
D. (d)`(pi R^(4))/4 sigma omega`

Answer

D

Explanation

`dq=sigma 2 pi x dx , dI=(dq)/(dt)=(sitma 2 pi x . Dx)/(2 pi //omega)=sigma omega x dx `
`dM=d I (pi x^(2))=pi sigma omega x^(3) dx, M=int_(0)^(R)dM=1/4piR^(4)sigma omega`