Electric Potential Video Lessons

Concept

# Problem: A -10.0nC point charge and a +20.0nC point charge are 15.0cm apart on the x-axis.a) What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero? b) What is the direction of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

###### FREE Expert Solution

Electric field:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{q}}{{\mathbf{r}}^{\mathbf{2}}}}$

Electric potential:

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

(a)

The point with zero potential is located between the two charges. Let the point be x m from the -10.0nC point charge

r10 = x m

r20 = (d - x) m, where d is the separation of the two point charges.

d = 15 cm(1m/100cm) = 0.15 m

q1 = -10.0 nC (10-9C/1nC) = -10.0 × 10-9 C

q2 = 20.0 nC (10-9C/1nC) = 20.0 × 10-9 C

$\begin{array}{rcl}{\mathbf{V}}_{\mathbf{1}}\mathbf{+}{\mathbf{V}}_{\mathbf{2}}& \mathbf{=}& \mathbf{0}\\ \mathbf{-}{\mathbf{V}}_{\mathbf{1}}& \mathbf{=}& {\mathbf{V}}_{\mathbf{2}}\\ \mathbf{-}\frac{\overline{)\mathbf{k}}{\mathbf{q}}_{\mathbf{1}}}{{\mathbf{r}}_{\mathbf{10}}}& \mathbf{=}& \frac{\overline{)\mathbf{k}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}_{\mathbf{20}}}\\ \mathbf{-}\frac{\mathbf{-}\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{×}\overline{){\mathbf{10}}^{\mathbf{-}\mathbf{9}}}}{\mathbf{x}}& \mathbf{=}& \frac{\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{×}\overline{){\mathbf{10}}^{\mathbf{-}\mathbf{9}}}}{\mathbf{0}\mathbf{.}\mathbf{15}\mathbf{-}\mathbf{x}}\\ \mathbf{0}\mathbf{.}\mathbf{15}\mathbf{-}\mathbf{x}& \mathbf{=}& \mathbf{2}\mathbf{x}\\ \frac{\mathbf{0}\mathbf{.}\mathbf{15}}{\mathbf{3}}& \mathbf{=}& \mathbf{x}\end{array}$

100% (96 ratings)
###### Problem Details

A -10.0nC point charge and a +20.0nC point charge are 15.0cm apart on the x-axis.

a) What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

b) What is the direction of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Electric Potential concept. You can view video lessons to learn Electric Potential. Or if you need more Electric Potential practice, you can also practice Electric Potential practice problems.