Question

Two point charges +q and –q each of mass m are revolving in a circle of the radius R. under mutual electrostatic force total energy of the system is (consider only electrostatic force)
$\begin{align}
  & A.\text{ }\dfrac{-{{q}^{2}}}{16\pi {{\varepsilon }_{0}}R} \\
 & B.\text{ }\dfrac{-{{q}^{2}}}{8\pi {{\varepsilon }_{0}}R} \\
 & C.\text{ }\dfrac{{{q}^{2}}}{16\pi {{\varepsilon }_{0}}R} \\
 & D.\text{ }\dfrac{-{{q}^{2}}}{4\pi {{\varepsilon }_{0}}R} \\
\end{align}$

Answer 1

Hint: It is given in the question that we have to consider electrostatic force between charges by taking that in mind we know that the electric force between stationary charged bodies is conventionally known as the electrostatic force. So in this case we will consider potential energy as total energy of the system.

Formula used:
${{U}_{E}}=\dfrac{k{{q}_{1}}{{q}_{2}}}{r}$

Complete step by step solution:
We know that total energy of system is given by
Total energy = potential energy + kinetic energy

It is given in the question that we have to consider only electrostatic force and we know that electric force between stationary charged bodies is conventionally known as the electrostatic force.

So in this case kinetic energy will be taken as zero. Hence we have to consider only potential energy as total energy of the system.

Now maximum distance between two point charges is,
$R+R=2R$

Now total energy is,
$\begin{align}
  & \Rightarrow T.E={{U}_{E}} \\
 & \Rightarrow T.E=k\dfrac{\left( -a \right)\left( a \right)}{2R} \\
 & \therefore T.E=\dfrac{-{{q}^{2}}}{8\pi {{\varepsilon }_{0}}R} \\
\end{align}$
Where,
${{U}_{E}}=$ Electric potential energy
k = coulomb constant
${{q}_{1}}{{q}_{2}}$ = charges
R = distance between the charges.

Hence option (B) is correct.

Additional information:
Definition of electrostatic force:
$\to $The electrostatic force is an attractive and repulsive force between particles due to their electric charges.
$\to $It is also known as Coulomb’s force.
$\to $The electric force between stationary charged bodies is conventionally known as the electrostatic force. Hence bodies have to be in steady positions.

Note:
When both charges revolve and there’s no stationary condition then we have to consider a total energy as kinetic energy. But in the provided solution we have considered stationary conditions. Hence in the given solution kinetic energy is taken is zero.