Question

The potential difference between two points $A$ and $B$ is

• A. Zero
• B. $\frac{Q}{4\pi {ϵ}_{0}a}(1-\frac{1}{\sqrt{5}})$
• C. $\frac{Q}{2\pi {ϵ}_{0}a}[1-\frac{1}{\sqrt{5}}]$
• D. $\frac{Q}{4\pi {ϵ}_{0}a}[2-\frac{1}{\sqrt{5}}]$

Answer 1

The correct option is C $\frac{Q}{2\pi {ϵ}_{0}a}[1-\frac{1}{\sqrt{5}}]$

Distance from $A$ to $-Q$ and $B$ to $+Q=\sqrt{a^2+4a^2}=\sqrt{5}a$
Potential difference
$\Delta V=V_A-V_B$
$=[\frac{kQ}{a}-\frac{kQ}{\sqrt{5}a}]-[\frac{kQ}{\sqrt{5}a}-\frac{kQ}{a}]$
$=\frac{2kQ}{a}[1-\frac{1}{\sqrt{5}}]$
$\Delta V=\frac{Q}{2\pi {ϵ}_{0}a}(1-\frac{1}{\sqrt{5}})$