Point P is at a distance of `r(gtR)` from the axis of the cylinder. The volume charge densilty and radius of this cylinder are n and r respectively

What is the electric field at point P?

Options

A. `(rhoR^(2))/(2 epsilon_(0)r)`
B. `(rhoR^(2))/(2 epsilon_(0))`
C. `(rhoR^(2))/(epsilon_(0)r)`
D. `(rhoR^(2))/(epsilon_(0))`

Answer

A

Explanation

`oint vecE.dvecA=q/(epsilon_(0))`
let l be the length of the cylinder.
Total charge on the cylinder `q=r(pR^(2)l)`
`impliesE(2pirl)=(rho pi R^(2)l)/(epsilon_(0))`
`impliesE=(rho R^(2))/(2 epsilon_(0)r)`