E field and potential

This diagram shows the electric field lines for a dipole. The dashed lines show lines of equal potential for this system. Notice that the equipotential lines are always perpendicular to the E field lines.

Recall the relationship between the electric field and the electric potential.

The change in potential is the negative integral of the electric field over a distance.

The electric field is the negative gradient of the potential.

In a one-dimensional case, the negative slope of the potential gives us the E field, as we can see in this graphical representation. Similarly, if we know the electric field as a function of x, we can find the potential by finding the negative area under the curve of the E field.

We can also analyze an electric field by plotting equipotential curves on a grid. Here, the grid squares are 1 cm x 1 cm. The blue dashed lines are equipotential curves.

Estimate the E field strength and direction at points A, B and C.

Recall that the electric field is zero everywhere inside a conductor in electrostatic equilibrium. Since E = 0 everywhere, the change in potential must also equal zero. In other words, any two points inside a conductor in electrostatic equilibrium are at equal potential.

The sum of the potential differences around a closed loop equals zero is a statement known as Kirchhoff's loop law. It is basically a statement of conservation of energy. A charge that moves all the way around a loop will have the same potential as when it started.