Question

An electron is observed to accelerate in the +z direction with an acceleration of $\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{16}}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. Explain how to use the definition of electric field to determine the electric field at this location, and give the direction and magnitude of the field.

Short answer

The magnitude of electric field is $9.1\times {10}^4\mathrm{N}/\mathrm{C}$and its direction is in the$\left(-\stackrel{⏜}{k}\right)$ or negative z axis.

Step-by-step solution

Identification of given data

The given data can be listed below,

• The acceleration of electron in +z direction is,$a=1.6\times {10}^{16}\mathrm{m}/{\mathrm{s}}^2$ .

Concept/Significance of Electric field.

When a charge exists in any form, the electric field is an electric property associated with each point in space.

The value of E, also known as electric field strength or simply the electric field, describes the size and direction of the electric field.

Determination of the direction and magnitude of the electric field.

According to Newton’s law and definition of electric field, the electric field is given by,

$$\begin{gathered} \overrightarrow{E}=\frac{\overrightarrow{F}}{q} \\ =\frac{m\overrightarrow{a}}{q} \end{gathered}$$

Here, m is the mass of the electron whose value is $9.1\times {10}^{-31}\mathrm{kg}$, a is the acceleration of the electron and q is the charge on the electron whose value is$-1.6\times {10}^{19}\mathrm{C}$.

Substitute all the values in the above,

role="math" localid="1656922370769" $$\begin{gathered} \overrightarrow{E}=\frac{\left(9.1\times {10}^{-31}kg\right)\left(1.6\times {10}^{16}m/s^2\stackrel{⏜}{k}\right)}{-1.6\times {10}^{-19}\mathrm{C}}\left(\frac{1\mathrm{N}}{1\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}\right) \\ =9.1\times {10}^4\mathrm{N}/\mathrm{C}\left(-\stackrel{⏜}{\mathrm{k}}\right) \end{gathered}$$

Thus, the magnitude of electric field is $9.1\times {10}^4\mathrm{N}/\mathrm{C}$and its direction is in the$\left(-\stackrel{⏜}{\mathrm{k}}\right)$ or negative z axis.