Question

A particle with charge +1nC (a nanocoulomb is 1X10^-9C) is located at the origin. What is the electric field due to this particle at a location $<0.1,0,0>\mathit{m}$?

Short answer

The electric field due to this particle at a location is $9.0\times {10}^{2}N/C$ .

Step-by-step solution

Identification of the given data

The given data can be listed below as:

• The electric charge on a particle is, $q=1\times {10}^{-9}C$.
• The location of the charged particle is, .
• The location of another point is, .

Significance of electric field

Due to a specific point charge, the electric field exists in a spherical area surrounding the point charge. The value of the electric field depends inversely on the distance from the specific point charge.

Determination of the position vector from the origin to the specified location

The expression of the position vector from the origin to the specified location can be expressed as:

Here, $\stackrel{\rightharpoonup }{r}$represents the position vector from the origin to the specified location.

Substitute all the values in the above equation.

Determination of the magnitude of the distance from the origin to the specified location

The magnitude of the distance from the origin to the specified location can be calculated as:

$\begin{array}{rcl}r& =& \left|\stackrel{\rightharpoonup }{r}\right|\\ & =& \sqrt{{\left(0.1m\right)}^2+{\left(om\right)}^2+{\left(0m\right)}^2}\\ & =& 0.1m\end{array}$

Determination of the electric field due to this particle at a location <0.1,0,0>m

The expression of the electric field due to this particle at a location can be expressed as:

$E=k\left(\frac{q}{r^2}\right)$

Here, E represents the required electric field due to this particle at a location and k represents the Coulomb’s constant whose value is $9\times {10}^{9}N.m^2/C^2$.

Substitute the values in the above equation.

$\begin{array}{rcl}E& =& \left(9\times {10}^{9}N.m^2/C^2\right)\left[\frac{1\times {10}^{-9}C}{{\left(0.1m\right)}^2}\right]\\ & =& 9.0\times {10}^{2}N/C\end{array}$

Hence, the electric field due to this particle at a location is $9.0\times {10}^{2}N/C$.