Q143 / 160 · TS EAMCET 2023 (13 May Shift 2) · Physics

Two conducting spheres of radii $r_1$ and $r_2$ are charged to the same surface charge density. The ratio of electric fields near their surfaces is

A
$\frac{r_1^2}{r_2^2}$
B
$\frac{r_2^2}{r_1^2}$
C
$\frac{r_1}{r_2}$
Correct answer
D
$1: 1$

Solution

$\begin{aligned} & \text { Given, } \sigma_1=\sigma_2 \\ & \frac{\mathrm{Q}}{4 \pi \mathrm{r}_1^2}=\frac{\mathrm{Q}}{4 \pi \mathrm{r}_2^2} \\ & \Rightarrow \frac{\mathrm{Q}}{4 \pi \in_0 \mathrm{r}_1^2}=\frac{\mathrm{Q}}{4 \pi \in_0 \mathrm{r}_2^2} \\ & \mathrm{E}_1=\mathrm{E}_2 \\ & \therefore \frac{\mathrm{E}_1}{\mathrm{E}_2}=\frac{1}{1}\end{aligned}$

Hence, the correct answer is option: 'D'.

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