Within a spherical charge distribution of charge density `rho(r)`, N equipotential surface of potential `V_(0), V_(0)+DeltaV, V_(0)+2DeltaV, … V_(0)+NDeltaV (DeltaV gt 0)`, are drawn and have increasing radii `r_(0), r_(1), r_(2), …. R_(N)`, respectively. If the difference in the radii of the surface is constant for all values of `V_(0)` and `DeltaV` then :-

Options

A. `rho(r )` = constant
B. `rho(r ) prop 1/(r^2)`
C. `rho(r ) prop 1/(r)`
D. `rho(r ) prop r`

Answer

C

Explanation

We know `E = (dV)/(dr)` Here, `Delta V and Delta r` are same for any pair of surfaces.

So, E = constant

Now, electric field inside the spherical charge distribution, `E = (rho)/(3 epsilon_0) r`
E would be constant if `rho r` = constant `implies rho(r ) prop 1/r`.