Electric field in a region of space is radially outward from origin and varies with distance 'r' from origin as E = kr. Find the charge enclosed in a sphere of radius 'a' centred at origin.

Explanation

Consider a sphere of radius a centred at origin. The electric field at its surface is `E = ka` ( radially outwards ) . On the surface area vector and electric field vector are parallel.

`implies phi_("total") int vec(E).bar(dA)= E int dA = (ka) xx ( 4pi a^(2))`
`implies phi = 4 kpi a^(3) `. By Gauss' law, `phi = ( q_(enc))/(epsilon_(0))`
`implies q_(enc) = 4 k epsilon_(0)pi a^(3)`