Question

What is the electric potential at a location $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{\hspace{0.33em}}\mathbf{m}$from an electron?

Short answer

The value of electric potential is $0.57\hspace{0.33em}\mathrm{V}$.

Step-by-step solution

Identification of given data

The given data can be listed below,

• The location of electron is, $\mathrm{r}=2.5\times {10}^{-9}\hspace{0.33em}\mathrm{m}$

Concept/Significance of electric potential

The effort done by the field in moving unit positive charge from the reference point to the place where potential is to be found determines electric potential at any point in the field.

Determination of the electric potential of electron

The potential of electron is given by,

$\mathrm{V}=\frac{\mathrm{Kq}}{\mathrm{r}}$

Here, K is the coulomb constant whose value is $9\times {10}^9\hspace{0.33em}\mathrm{N}.{\mathrm{m}}^2/{\mathrm{C}}^2$ , q is the charge on the electron whose value is $-1.6\times {10}^{-19}\mathrm{C}$ , and r is the distance between location and electron.

Substitute all the values in the above expression.

role="math" localid="1657098419012" $$\begin{gathered} \mathrm{V}=\frac{\left(9\times {10}^9\hspace{0.33em}\mathrm{N}.{\mathrm{m}}^2/{\mathrm{C}}^2\right)\left(-1.6\times {10}^{-19}\mathrm{C}\right)}{2.5\times {10}^{-9}\mathrm{m}} \\ =0.57\mathrm{V} \end{gathered}$$

Thus, the value of electric potential is $0.57\hspace{0.33em}\mathrm{V}$.