Question

At a particular location in the room there is an electric field $<1000,0,0>\mathbf{ }\mathbf{\text{N/C}}$. Where would you place a single negative point particle of charge $\mathbf{1}\mathit{\mu }\mathit{C}$in order to produce this electric field?

Short answer

The position of charge to produce electric field $\left|\overrightarrow{r}\right|=\left(3,0,0\right) \text{m}$.

Step-by-step solution

Identification of given data

• The value of electric field.
• The value of point charge particle$q=1 \times {10}^{-6}\text{C}$.

Electric field

The electric field is the property of every point when charge is present in any form.

The electric field inside a sphere of uniform charge is calculated by

$\overrightarrow{\mathbf{E}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{4}\mathbf{\pi }{\mathbf{\epsilon }}_{\mathbf{0}}}\mathbf{·}\frac{\mathbf{q}}{{\left|\overrightarrow{r}\right|}^{\mathbf{2}}}\hat{\mathbf{r}}$

Here, = Electric field, q= Charge, $\frac{\mathbf{1}}{\mathbf{4}\mathbf{\pi }{\mathbf{\epsilon }}_{\mathbf{0}}}\mathbf{=}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{ }\mathbf{ }\mathbf{\text{N}}\mathbf{·}{\mathbf{\text{m}}}^{\mathbf{\text{2}}}{\mathbf{\text{/C}}}^{\mathbf{\text{2}}}$and r= radius of the sphere

Calculation of the electric field position

The position is calculating by using,

$\overrightarrow{E}=\frac{1}{4\pi {\epsilon }_0}·\frac{q}{{\left|\overrightarrow{r}\right|}^2}\hat{r}$

Substituting the values,

role="math" localid="1668507954643"

Thus, position is $\left|\overrightarrow{r}\right|=\left(3,0,0\right) \text{m}$.