Question

A charge of $30\mu C$ is at the reference point in the $X$ -Y coordinate system. Calculate the potential difference between the points $(\frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}})$ and $(a,0)$

Answer 1

$\begin{array}{cc}AO=\sqrt{{(\frac{a}{\sqrt{2}}-0)}^2+{(\frac{a}{\sqrt{2}}-0)}^2}& \\ AO=\sqrt{\frac{a^2}{2}+\frac{a^2}{2}}& \\ AO& =\sqrt{\frac{2a^2}{2}}\\ AO& =a\\ OB& =\sqrt{(a-0{)}^2+(0-0{)}^2}\\ OB& =a\end{array}$
Potential at point $A$
$V_A=\frac{kq}{AO}$
$V_A=\frac{kq}{a}$
Potential at point $B$
$\begin{array}{c}{V}_B=\frac{kq}{BO}\\ V_B=\frac{kq}{a}\end{array}$
$V_B-V_A=\frac{kq}{\alpha }-\frac{kq}{\alpha }$
$V_B-V_A=0$
Potential difference $=0$