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)prop1/(r^(2))`
C. `rho(r)prop1/r`
D. `rho (r)propr`

Answer

C

Explanation

As we know electric field `E=(-dV)/(dr)`
E=constant `:.dv` and dr same
`E=(K_(phi))/(r^(2))=c`
`impliesphipropr^(2)`
`:.phi=int_(0)^(r)rho 4pir^(2)drimpliesrho prop 1/r`