Question

The electrostatic potential energy of two point charges, $1\mu C$each, placed 1 meter apart in air is?
A. $9\times {{10}^{3}}J$
B. $9\times {{10}^{9}}J$
C. $9\times {{10}^{-3}}J$
D. $9\times {{10}^{-3}}eV$

Answer 1

Hint: An electric potential which is also known as the electric field potential, potential decrease, or electrostatic potential is the net – work done to move a unit charge from a point to a particular point under the influence of some electric field with zero acceleration. This question can easily be solved by using a simple formula of electrostatic potential energy between the two point charges. This formula can easily be derived by using Coulomb's law.

Formula used:
For solving the given question, we will be using the formula of Electrostatic potential energy, i.e.,
Electrostatic potential energy $=U=\dfrac{k{{q}_{1}}{{q}_{2}}}{r}$

Complete step-by-step answer:

By using the above-given formula for Electrostatic potential energy, we have
Electrostatic potential energy $=U=\dfrac{k{{q}_{1}}{{q}_{2}}}{r}$
Where k is the Coulomb’s constant, $k=8.9875517923\times {{10}^{9}}~kg\cdot {{m}^{3}}\cdot {{s}^{-}}^{2}\cdot {{C}^{-}}^{2}$
For the sake of calculation, we will use $k=9\times {{10}^{9}}~kg\cdot {{m}^{3}}\cdot {{s}^{-}}^{2}\cdot {{C}^{-}}^{2}$
And, ${{q}_{1}}$ and ${{q}_{2}}$ are the two point charges in this case,
${{q}_{1}}={{q}_{2}}=1\mu C$
Now,
${{q}_{1}}={{q}_{2}}=1\times {{10}^{-6}}C$
And, r is the distance between the two point charges, in this case
$r=1m$
Now, by using the given data in the electrostatic potential energy formula
$U=\dfrac{k{{q}_{1}}{{q}_{2}}}{r}$
\[\Rightarrow U=\dfrac{9\times {{10}^{9}}\times 1\times {{10}^{-6}}\times 1\times {{10}^{-6}}}{1}J\]
\[\Rightarrow U=\dfrac{9\times {{10}^{9}}\times 1\times {{10}^{-12}}}{1}J\]
\[\Rightarrow U=\dfrac{9\times {{10}^{9-12}}\times 1}{1}J\]
\[\Rightarrow U=9\times {{10}^{-3}}J\]
So, the electrostatic potential energy of two point charges, $1\mu C$ each, placed 1 meter apart in air is $9\times {{10}^{-3}}J$

So, the correct answer is “Option C”.

Note: A coulomb is defined as the volume of electricity transported by a current of one ampere in a single second.
\[1C=6.24\times {{10}^{18}}electrons\](Approximately)
The unit is named after Charles-Augustin de Coulomb, a French physicist who was active during the late 19th to mid 20th century. Electrostatic Potential energy is the reason why lightning happens.