Question

An infinite conducting sheet has surface charge density $\sigma $ . The distance between two points is $r$ . The potential difference $\left(V_{A} - V_{B}\right)$ between these points is

• A. $\frac{\sigma r}{2 \epsilon _{0}}$
• B. $\frac{\sigma r}{\epsilon _{0}}$
• C. $\frac{\sigma }{\epsilon _{0} r}$
• D. $\frac{\sigma }{2 \epsilon _{0} r}$

Answer 1

Answer: (A)

$V_{A}-V_{B}=\displaystyle \int _{a}^{b} E . d r=E \, \left(b - a\right)=\frac{\sigma \, r}{2 \left(\epsilon \right)_{0}}$