Equipotential Surface of Various Charge System

The potential of a field at any point is the function of its distance from the source charge and it tells about the strength of the field at that point.

For a point charge, the potential of each point lying at an equal distance from the charge will have the same potential.

These points around a charge constitutes a surface called an equipotential surface.

Let's see the equipotential surfaces for different configuration of charges.

For a point charge, the equipotential surface will be spherical with the charge at its center.

But if we have a dipole or other configuration of charges, the relation of potential with distance from the charge can vary in different directions.

Thus, the equipotential surfaces around these charge configurations can have different shapes.

Let's see the equipotential surface for a dipole

The dipole is a system of two equal and opposite charges separated by a distance. The electric field lines of a dipole look like this

And if we draw the equipotential surface for the dipole, we will have to put a normal on these lines where potential are equal.

After joining the normals on the points of equal potential, we will get an equipotential surface.

In the figure, we can see that the equipotential surfaces are closer in the region where the field lines are more crowded.

This is because, the electric potential depends directly on the electric field.

And so, the points of equal potential lie nearer in the region, where the field lines are more crowded

So, it is now understood that the equipotential surface depends on the configuration of electric field lines in the space.

Let's see the equipotential surface of two like charges

If we consider a system of two negative charges, their field lines will look like this

In the region between the charges, the field lines are negligible. The equipotential surface of the system is shown in green lines.

Similarly, for the different system of charges, the equipotential surface can have different shapes.

Let's see the equipotential surface of a uniform field.

For a uniform electric field, the field lines will be parallel and equidistant from each other.

At any point on the plane, normal to this field will have the same potential as each point on the plane will lie at the same distance from the source of the field.

Here A, B and C are three different equipotential surfaces with different potentials.

So, we have seen that the equipotential surface of a uniform field will be a plane perpendicular to the field.

Revision

Equipotential surface of a point charge is spherical with the charge at the center of the sphere.

Equipotential surface of a dipole looks like

The equipotential surface of two like charges are looks like

Equipotential surfaces in the uniform electric field look like a sheet.

The End