Electric Field Principles

Discussion of Principles

The potential difference between two points is defined to be the work per unit charge required to move a small, positive test charge between the two points.

Any two points which have zero potential difference are said to lie on an equipotential surface. The amount of work required to move a small positive test charge between these two points is zero; hence any force acting on the test charge must always point perpendicular to this surface. Since the force per unit charge on the test charge is defined to be the electric field, we see that the electric field is always perpendicular to equipotential surfaces.

It turns out that the electric field is equal to the gradient of the electric field.

Note that the electric field is proportional to a force; hence, the electric field is a vector quantity. The electric potential is proportional to work, and therefore is a scalar quantity.

Example

In the figures below, the electric field and equipotential lines are illustrated for a dipole distribution - i.e., a charge distribution consisting of positive and negative point charges separated by some distance, and where the net charge of the distribution is zero.

Notes:

instead of indicating field strength with vector size (which would produce a messy diagram), color is used in the electric field diagram above.
The electric field plot above illustrates the actual electric field vectors - not electric field lines. Electric field vectors are everywhere tangent to electric field lines.
The equipotential lines are not labeled according to voltage (again, for lack of room in the display window). In laboratory, you will want to label each equipotential line with its voltage value measured with your voltmeter.
In this lab, we will use a "conducting paper" to establish small currents which lead to voltages that you measure with a voltmeter. This turns out to give equipotential lines (and corresponding electric field lines) which mimic the true fields that exist around actual three-dimensional conducting electrodes. Real electrodes charged in vacuum or air require no such currents - electric fields and equipotential lines exist when no currents flow between the electrodes.

Question

In the electric field diagram above, there is a red charge and a blue charge. Which one is positive, and which is negative?