An infinity long cylinder of radius R has an infinitely long cylindrical cavity of radius `(R)/(2)` are shown in the figure. The remaining portion has uniform volume charge density `rho`. The magnitude of electrical field at the centre of the cavity is-

Options

A. `(rhoR)/(6epsilon_(0))`
B. `(rhoR)/(4epsilon_(0))`
C. `(rhoR)/(2epsilon_(0))`
D. `(rhoR)/(3epsilon_(0))`

Answer

B

Explanation

Electric field in cavity is given as `=(rhor)/(2epsilon_(0))`
where `r` is distance between the axis of cylinder cavity
so, E in cavity `=(rho(R)/(2))/(2epsilon_(0))=(rhoR)/(4epsilon_(0))`