JEE Main 2023 · Physics · Electrostatics · hard

A uniformly charged solid non-conducting sphere of radius 10 cm carries a total charge of 8 nC. Taking (1)/(4πε0)=9×10^9 N m^2 C^-2 and the potential…

Numerical answer

A uniformly charged solid non-conducting sphere of radius

10\ \mathrm{cm}

carries a total charge of

8\ \mathrm{nC}

. Taking

\dfrac{1}{4\pi\varepsilon_0}=9\times10^{9}\ \mathrm{N\,m^2\,C^{-2}}

and the potential at infinity as zero, the electric potential (in V) at a point

5\ \mathrm{cm}

from the centre is

Show answer and solution

Answer: 990

Outside,

E=\dfrac{kQ}{r^2}

; inside,

E=\dfrac{kQr}{R^3}

. Potential at the surface:

\dfrac{kQ}{R}=\dfrac{9\times10^9\times8\times10^{-9}}{0.1}=720\ \mathrm V

. Inside,

V(r)=\dfrac{kQ}{2R^3}(3R^2-r^2)

; at

r=R/2

V=\dfrac{kQ}{R}\cdot\dfrac{3-\tfrac14}{2}=720\times1.375=990\ \mathrm V

. (Equivalently,

V=720+\int_{R/2}^{R}E\,dr=720+270

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