# Problem: Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively. Where should a third charge of +3.0- μC be placed on the +x-axis so that the potential at the origin is equal to zero? A) x = 3.0 cm B) x = 5.0cm C) x = 1.0cm D) x = 2.0 cm  E) x = 4.0cm

###### FREE Expert Solution

Potential due to point charge is expressed as:

$\overline{){{\mathbf{V}}}_{{\mathbf{p}}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{q}}{\mathbf{r}}}$

The net potential at the origin is due to three charges:

$\begin{array}{rcl}{\mathbf{V}}_{\mathbf{0}}& \mathbf{=}& {\mathbf{V}}_{\mathbf{1}}\mathbf{+}{\mathbf{V}}_{\mathbf{2}}\mathbf{+}{\mathbf{V}}_{\mathbf{3}}\\ & \mathbf{=}& \frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}}{{\mathbf{r}}_{\mathbf{1}}}\mathbf{+}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}_{\mathbf{2}}}\mathbf{+}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{3}}}{{\mathbf{r}}_{\mathbf{3}}}\\ & \mathbf{=}& \mathbf{k}\mathbf{\left(}\frac{{\mathbf{q}}_{\mathbf{1}}}{{\mathbf{r}}_{\mathbf{1}}}\mathbf{+}\frac{{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}_{\mathbf{2}}}\mathbf{+}\frac{{\mathbf{q}}_{\mathbf{3}}}{{\mathbf{r}}_{\mathbf{3}}}\mathbf{\right)}\end{array}$

97% (281 ratings) ###### Problem Details

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively. Where should a third charge of +3.0- μC be placed on the +x-axis so that the potential at the origin is equal to zero?

A) x = 3.0 cm B) x = 5.0cm C) x = 1.0cm D) x = 2.0 cm  E) x = 4.0cm