Question

Statement I: The surface charge densities of two spherical conductors of different radii are equal. Then the electric field intensities near their surface are also equal.
Statement II:Surface charge density is equal to charge per unit area.

• A. If both statements are true and statement II is correct explanation of statement I.
• B. If both statements are true but statement II is not the correct explanation of statement I.
• C. If statement I is true but the statement II is false.
• D. If both statements are false.

Answer 1

Answer: (B)

As ${\sigma }_1={\sigma }_2$ (Given)
$\therefore \frac{q_1}{4\pi r_1^2}=\frac{q_2}{4\pi r_2^2}$, or $\frac{q_1}{q_2}=\frac{r_1^2}{r_2^2}$ [Let $r_1$ and $r_2$ be two different radii]
Then the ratio of electric field intensities near the surface of spherical conductor,
$\frac{E_1}{E_2}=\frac{q_1}{4\pi {\epsilon }_0{r}_1^2}\times \frac{4\pi {\epsilon }_0{r}_2^2}{q_2}=\frac{q_1}{q_2}\times \frac{r_2^2}{r_1^2}=1$, i.e., $E_1=E_2$