Question

What is the ratio of the charges of two conducting spheres of radii r₁ and r₂ which have equal surface charge density?

Options

• ${\displaystyle \frac{{\text{r}}_1^2}{{\text{r}}_2^2}}$

• ${\displaystyle \frac{{\text{r}}_2^2}{{\text{r}}_1^2}}$

• ${\displaystyle \frac{{\text{r}}_1}{{\text{r}}_2}}$

• ${\displaystyle \frac{{\text{r}}_2}{{\text{r}}_1}}$

Answer 1

${\displaystyle \frac{{\text{r}}_1^2}{{\text{r}}_2^2}}$

Explanation:

${\displaystyle \text{Here,} {\sigma }_1={\sigma }_2}$

${\displaystyle \therefore \frac{{\text{q}}_1}{4{\pi }_1^2}=\frac{{\text{q}}_2}{4\pi {\text{r}}_2^2}\Rightarrow \frac{{\text{q}}_1}{{\text{q}}_2}=\frac{{\text{r}}_1^2}{{\text{r}}_2^2}}$