Question

1. If you are given an equipotential diagram, how could you use it to figure out the direction of the electric field at a specific location? Explain your thinking in detail, using both words and a picture.

2. If you are given an equipotential diagram, how could you use it to figure out which regions have a stronger electric field and which regions have a weaker electric field? Explain your thinking in detail, using both words and a picture.

Answer 1

1. The direction of electric field E is always normal to the eqipotential surface, because if the electric field is making any angle other than 90^o, the we must do some work in tranfering a charge from one point to other (from A to B) over the equipotential surface. But no work is done in moving a charge between two points on an equipotential surface as the potential difference between any two points on an equipotential surface is zero. Hence, the electric field direction will be perpendicular to the equipotential diagram.

2. We can also determine the strength of electric field from the equipotential diagram. In regions of weak field the equipotential surfaces will be further apart while in regions of strong field the equipotentials are closely spaced. This follows from the relationship between electric field E and potential difference dV as, E = - dV/dr, dV/dr = potential gradient, that is, change in potential difference with distance.