Question

The radii of two conducting sphere are $a$ and $b$. They are charged by equal charge density. What would be the ratio of the electric field intensities at their surface?

• A. $b^2:a^2$
• B. $1:1$
• C. $a^2:b^2$
• D. $b:a$

Answer 1

Answer: (B)

$1:1$

$1:1$

${\sigma }_1={\sigma }_2$

$\frac{q_1}{4\pi a^2}=\frac{q_2}{4\pi b^2}$

$\therefore \frac{q_1}{q_2}=\frac{a^2}{b^2}$

$\Rightarrow \frac{E_1}{E_2}=\frac{\frac{1}{4\pi {\epsilon }_0}\frac{q_2}{a^2}}{\frac{1}{4\pi {\epsilon }_0}\frac{q_2}{b^2}}=\frac{b^2}{a^2}\times \frac{q_1}{q_2}$

$\therefore \frac{E_1}{E_2}=\frac{b^2}{a^2}\times \frac{a^2}{b^2}=\frac{1}{1}=1:1$