JEE Main 2016 · 10 Apr · Shift 1 · Physics Q12

← JEE Main 2016 · 10 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 12 of 90

Within a spherical charge distribution of charge density ρ(r), N equipotential surfaces of potential $V_0$ , $V_0+\Delta V$ , $V_0+2\Delta V$ , .......... $V_0+N\Delta V$ (ΔV > 0), are drawn and have increasing radii $r_0$ , $r_1$ , $r_2$ , .......... $r_N$ , respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and ΔV then :

\rho(r)\propto r

\rho(r)=

constant

\rho(r)\propto\dfrac1r

\rho(r)\propto\dfrac1{r^2}

Answer and worked solution

Official answer: C

Equal steps in V at equal steps in r mean E is constant. For a spherical distribution $E=\frac{Q(r)}{4\pi\epsilon_0r^2}$ , so $Q(r)\propto r^2$ and $\rho=\frac1{4\pi r^2}\frac{dQ}{dr}\propto\frac1r$ .

Topics:Equipotential surfaces Electric flux and Gauss's law

← Previous question Next question →

JEE Main 2016 · 10 Apr · Shift 1, Physics question 12