There are two co-axial non conducting cylinders of radii a and `b (gt a)`. Length of each cylinder is `L (gtgt b)` and their curved surfaces have uniform surface charge densities `of – sigma` (on cylinder of radius a) and `+ sigma` (on cylinder of radius b). The two cylinders are made to rotate with same angular velocity `omega` as shown in the figure. The charge distribution does not change due to rotation. Find the electric field `(E )` and magnetic field (B) at a point (P) which is at a distance r from the axis such that (a) `0 lt r lt a` (b) `a lt r lt b` (c) `r gt b`. Assume that point P is close to perpendicular bisector of the length of the cylinders

Answer

`E=0 for r lt a`
`=(asigma)/(in_(0)r)` radially inward for `a lt r lt b`
`=((b-a))sigma)/(in_(0)r)` radially outward for `r lt b`
`B=sigmaomega(b-a)` up along the axis for `r lt a`
`=b sigmaomega` up along the axis for `a lt r lt b=0 for r lt b`