A non-conducting disc having unifrom positive charge `Q`, is rotating about its axis with unifrom angular velocity `omega`.The magnetic field at the centre of the disc is.

Options

A. directed outward
B. having magnitude `(mu_(0)Qomega)/(4piR)`
C. directed inwards
D. having magnitude `(mu_(0)Qomega)/(2piR)`

Answer

A, D

Explanation

Consider a ring of radius `x` and thickness `dx`.
Equivalent current in this ring `=omega/(2pi)xx"charge on ring "=omega/(2pi)xx(2pixxdx)Q/(piR^(2))`
`dB` (due to this ring )`=mu_(0)/(2x)(omega/(2pi)(2xQ)/R^(2)dx) :.B=underset(0)overset(R)int(mu_(0)omega)/(2pi) Q/R^(2)dx.`
`=(mu_(0)omegatheta)/(2piR^(2)).R=(mu_(0)Rtheta)/(2piR)`.