Question

An electron in a region in which there is an electric field experiences a force of magnitude $\mathbf{3}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{16}}\mathbf{}\mathbf{N}$ . What is the magnitude of the electric field at the location of the electron?

Short answer

The magnitude of the electric field at the location of electron is $2.3\times {10}^3\mathrm{N}/\mathrm{C}$.

Step-by-step solution

Identification of given data

The given data can be listed below,

The electric force experienced by electron is,$F_e=3.7\times {10}^{-16}\mathrm{N}$

Concept/Significance of electric force.

All charged particles are subject to an electric force. The electric force is responsible for a wide range of occurrences, like making your hair stand up on a cold, dry day, and causing your car to start.

Determination of the magnitude of the electric field at the location of the electron

The electric field related to the charge of electron is given by,

$\left|\stackrel{\rightharpoonup }{E}\right|=\frac{\left|\stackrel{\rightharpoonup }{F}\right|}{q_e}$

Here,$\left|\stackrel{\rightharpoonup }{F}\right|$is the magnitude of force and qis the magnitude of charge on the electron whose value is$1.6\times {10}^{-19}C$ .

Substitute all the values in the above expression,

role="math" localid="1656914428005" $$\begin{gathered} \left|\stackrel{\rightharpoonup }{\mathrm{E}}\right|=\frac{3.7\times {10}^{-16}\mathrm{N}}{1.6\times {10}^{-19}\mathrm{C}} \\ =2.3\times {10}^3\mathrm{N}/\mathrm{C} \end{gathered}$$

Thus, the magnitude of the electric field at the location of electron is $2.3\times {10}^3\mathrm{N}/\mathrm{C}$.