Question

A -3.0 nC charge is on the x-axis at x = -9 cm and a +4.0 nC

charge is on the x-axis at x = 16 cm. At what point or points on

the y-axis is the electric potential zero?

Short answer

The points on y-axis where the potential of electric is zero are $\pm 12cm$

Step-by-step solution

Total Potential 

The electric potential of charge q is $V=\frac{1}{4\pi e_0}\frac{q}{r}$

Therefore, the total potential for multiple point charges isrole="math" localid="1648129896992" $V=\sum _{}\frac{1}{4\pi e_0}\frac{q_i}{r_i}$

Calculation of electric Potential on y-axis

The total electric potential from distance y to x-axis is

$V=\frac{1}{4\mathrm{\pi }{\in }_0}\left(\frac{q_1}{r_1}+\frac{q_2}{r_2}\right)$

Therefore, the equation for y is

localid="1648299178540" $\begin{array}{rcl}\frac{3}{\sqrt{{\left(9cm\right)}^2+y^2}}& =& \frac{4}{\sqrt{{\left(16cm\right)}^2+y^2}}\\ 9\left({\left(16cm\right)}^2+y^2\right)& =& 16\left({\left(9cm\right)}^2+y^2\right)\\ 7y^2& =& 1008c{m}^2\\ y2& =& 144cm\\ & =& \pm 12cm\end{array}$

Thus, The points on the y-axis where the potential of electricity is zero are $\pm 12cm$