An insulated sphere of radius `r` haas a uniform volume charge density `lambda`. The electric field at a point `A`, which is at distance `r` from its centre is given by `(R gt r)`

Options

A. Zero
B. `R lambda//3 in_(0)`
C. `(2 r lambda)/(3 in_(0))`
D. `( r lambda)/(3 in_(0))`

Answer

D

Explanation

Charge enclosed by sphere of radius `r` is given by `q = (4)/(3) pi r^(3) lambda`, where `lambda` is volume density of charge.

According to Gauss's theorem,
`oint vec(E). Vec(ds) = (q)/(in_(0))` or `oint vec(E). vec(ds) = (4pi r^(3) lambda)/(3 in_(0))`
`E xx 4pi r^(2) = (4pi r^(3) lambda)/(3 in_(0))`
`E = (r lambda)/(3 in_(0))`