Two spherical conductors of capacities 3 and 2 are charged to same potential having radii 3 cm and 2 cm respectively. If ' σ₁ ' and ' σ₂ ' represent surface density of charge on respective conductors then (σ₁)/(σ₂) is (a) 1/3 (b) 1/2 (c) 2/3 (d) 3/4

Answer: (c). Same potential: Q = CV, and C ∝ r, so Q ∝ r. σ = (Q)/(4π r²) ∝ r/r² = 1/r (σ₁)/(σ₂) = (r₂)/(r₁) = 2/3 So the answer is (c) 2/3.

Two spherical conductors of capacities 3 and 2 are charged to same… | MHT CET 2023 (11 May, Shift 2)

Q10MHT CET 2023 · 11 MAY · SHIFT 2Medium

Capacitance of a Conductor

Two spherical conductors of capacities $3\ \mu\text{F}$ and $2\ \mu\text{F}$ are charged to same potential having radii $3\text{ cm}$ and $2\text{ cm}$ respectively. If ' $\sigma_1$ ' and ' $\sigma_2$ ' represent surface density of charge on respective conductors then $\frac{\sigma_1}{\sigma_2}$ is

Show answer and solution

Answer: (c)

Same potential: $Q = CV$ , and $C \propto r$ , so $Q \propto r$ .
$\sigma = \frac{Q}{4\pi r^2} \propto \frac{r}{r^2} = \frac{1}{r}$
$\frac{\sigma_1}{\sigma_2} = \frac{r_2}{r_1} = \frac{2}{3}$
So the answer is (c) $\frac{2}{3}$ .

Report a mistake

Capacitance of a Conductor question from MHT CET 2023 (11 May, Shift 2)

More questions on Capacitance of a Conductor