A sphere of charges of radius R carries a positive charge whose volume charge density depends only on the distance r from the ball's centre as `rho=rho_0(1-r/R),` where `rho_0` is constant. Assume epsilon as the permittivity of space.
The magnitude of electric field as a function of the distance r inside the sphere is given by

Options

A. `E=rho_0/epsilon[r/3-r^3/(4R)]`
B. `E=rho_0/epsilon[r/4-r^3/(3R)]`
C. `E=rho_0/epsilon[r/3+r^2(4R)]`
D. `E=rho_0/epsilon[r/4+r^2/(3R)]`

Answer

A

Explanation

According to Gauss's theorem
`E=(1/(4piepsilon_0)) (q_("in")/r^2)`……..i
for `rleR`
`q_(in)=int_0^r(4pir^2).dr.rho`
`=int_0^r(4pir^2)(rho_0)(1-r/2)dr`
`=4pirho_0(r^3/3-r^4/(4R))`
Substituting in eqn i we get
`E=(rho_0)/epsilon[r/3-r^2/(4r)]`