JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Electrostatics

Two metal spheres of radius

R

and

3 R

have same surface charge density

σ

. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes

σ_{1}

and

σ_{2}

, respectively. The ratio

\frac{σ _{1}}{σ _{2}}

is.

Answer: (D)

Solution

Each isolated sphere has potential

V = \frac{σ r}{ε _{0}}

written in terms of its surface density. On contact the spheres share charge until their potentials are equal, so

σ_{1} r_{1} = σ_{2} r_{2}

, giving

\frac{σ _{1}}{σ _{2}} = \frac{r _{2}}{r _{1}} = \frac{3 R}{R}

. The ratio

\frac{σ _{1}}{σ _{2}}

3

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option