Two spherical conductors of radii 4 cm and 5 cm are charged to the same potential. If ' σ₁ ' and ' σ₂ ' be the respective values of the surface density of charge on the two conductors then the ratio σ₁: σ₂ is (a) 5: 4 (b) 3: 2 (c) 4: 3 (d) 2: 1

Answer: (a). V = kq/r = (σ r)/(ε₀), so at equal V: σ ∝ 1/r. (σ₁)/(σ₂) = (r₂)/(r₁) = 5/4 So the answer is (a) 5: 4.

Two spherical conductors of radii 4 cm and 5 cm are charged to the… | MHT CET 2021 (22 Sep, Shift 2)

Q83MHT CET 2021 · 22 SEP · SHIFT 2Medium

Electric Potential & Equipotentials

Two spherical conductors of radii $4\text{ cm}$ and $5\text{ cm}$ are charged to the same potential. If ' $\sigma_1$ ' and ' $\sigma_2$ ' be the respective values of the surface density of charge on the two conductors then the ratio $\sigma_1 : \sigma_2$ is

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Answer: (a)

$V = \frac{kq}{r} = \frac{\sigma r}{\varepsilon_0}$ , so at equal $V$ : $\sigma \propto \frac{1}{r}$ .
$\frac{\sigma_1}{\sigma_2} = \frac{r_2}{r_1} = \frac{5}{4}$
So the answer is (a) $5 : 4$ .

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Electric Potential & Equipotentials question from MHT CET 2021 (22 Sep, Shift 2)

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