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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

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

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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?

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