Question

Two identical thin rings each of radius \[r\] are coaxillary placed at a distance \[r\] have equal charge \[q\] each. Work done in moving a charge \[q'\] from the center of one ring to that of the other is?
A. Infinity
B. \[\dfrac{{{q^2}}}{{4\pi {\varepsilon _0}r}}\]
C. Zero
D. \[\dfrac{{qq'}}{{4\pi {\varepsilon _0}r}}\]

Answer 1

Hint: First of all, we will find out the electric potential in the centers of both the rings. Word needs to be done in moving a charge from lower potential to the higher potential, in an electric field.

Complete step by step answer:
In the given question, we are supplied with the following data:
There are two identical thin rings which are of radius \[r\].
They are coaxillary placed at a distance \[r\] have equal charge \[q\] each.
We are asked to find the amount of work done in moving a charge \[q'\] from the center of one ring to that of the other.
Let us proceed to solve the problem.
Since the rings are similar and have the same charge, the electrical potential in the center of the two rings is equal. Therefore, zero is the potential difference between the centers of these rings.
So, we can say, \[V = 0\]
Therefore, the work performed to transfer a charge \[q'\] between these rings (centers) is

$W = - \dfrac{V}{q} \\
\Rightarrow W = \dfrac{0}{{q'}} \\
\Rightarrow W = 0\,{\text{J}} \\$

Hence, the required answer is zero joules.

So, the correct answer is “Option C”.

Additional Information:
Work done: In physics, through the application of force along a displacement, work is the energy transferred to or from an object. It is also represented as the product of force and displacement in its simplest form. A force is said to do positive work if it has a part (when applied) in the direction of the point of application's displacement.

Note:
Remember that the work done is equal to the energy transition. The work done against gravity, for example, is equal to the change in the body’s potential energy and the work done against all resistive forces is equal to the change in the overall energy. A force does negative work if at the point of application of the force it has a part opposite to the direction of the displacement.