Question

The potential (relative to a point at infinity) midway between two charges of equal magnitude and opposite sign is zero. Is it possible to bring a test charge from infinity to this midpoint in such a way that no work is done in any part of the displacement? If so, describe how it can be done. If it is not possible, explain why.

Short answer

Yes, Due to the symmetry of the graph

Step-by-step solution

About potential

The electric potential difference between points A and B, VB−VA is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge.Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

Determine the possibility of bringing  test charge  from infinity to this midpoint

Solution:

Yes, Due to the symmetry of the graph- It is possible to bring a test charge from infinity to the midpoint without dining any

Work on it in any part of the displacement The two charges will affect the test charge with the same force's magnitude and in

the opposite direction- 80, the point charge will move from in?nity to the midpoint without suffering any electric force on it

Therefore

Yes , Due to the symmetry of the graph