Question

Because electric field lines and equipotential surfaces are always perpendicular, two equipotential surfaces can never cross; if they did, the direction of E would be ambiguous at the crossing points. Yet two equipotential surfaces appear to cross at the centre of Fig. 23.23c. Explain why there is no ambiguity about the direction of Ein this particular case.

Short answer

The total energy is equal to zero, then there is no ambiguity about the direction of the total electric energy in this particular case

Step-by-step solution

About electric field lines 

Electric field lines are an excellent way of visualising electric fields. They were first introduced by Michael Faraday himself. A field line is drawn tangential to the net at a point. Thus at any point, the tangent to the electric field line matches the direction of the electric field at that point.

Determine why there is no ambiguity about the direction of E in this particular case

As We know the electric energy due to a point charge is given by

Calculation:

In order to evaluate the total electric energy, we use the following relation

Therefore the total energy is equal to zero, then there is no ambiguity about the direction of the total electric energy in this particular case