Question

A. If the electric field E is zero at a given point, must the electric potential V also equal zero at that point? Explain your reasoning and give an example to prove your answer.

B. A positive charge moves in the direction of a uniform electric field. Does its potential energy increase or decrease? Does the electric potential increase or decrease? Explain your reasoning.

C. If the electric potential at some point is zero, does it follow that there are no charges in the vicinity of that point? Explain your reasoning.

Answer 1

Sol:

A. It is not always true that if electric the electric field E is zero at a given point, must the electric potential V also equal zero at that point:
For example: If we have two sidentical electric charges separated by a finite distance, then the electric field at the midpoint of line joining the two charges is zero but electrical potential will not be zero at that point.

B. If a positive charge moves in the direction of a uniform electric field its potential energy decreases. Because electric line of force i.e. electric field lines are directed from high potential to low potential and positive charge moves in the same direction as electric field lines, hence positive charge also moves from high potential to low potential. Hence its potential energy is decreases.

C. If the electric potential at some point is zero, it does not mean that there are no charges in the vicinity of that point.

One good example of this is electric dipole. Electric dipole hase two equal and opposite charges and but at any point in the equatorial plane of dipole the electric potetial is zero.