Field at a Charged Surface


"Electric field lines must be perpendicular to the surface of a charge". How can we explain this in terms of force or energy? What will it be like if the electric field lines are not perpendicular to the surface of the charge?


Here are some ideas. Technically charges do not have surfaces. Charged objects do. If an object is charged, say negatively for example, then there are an excess of electrons in or on the object. Since like charges repel each other there will be a tendency for the electrons to distribute themselves in such a way that the arrangement has minimum potential energy. Any other arrangement would result in unbalanced forces on some or all of the electrons, causing them to shift about until the minimum energy configuration is achieved.

If the lines of the electric field at the surface of the object were not perpendicular to the surface we could resolve the force vectors resulting from the interaction of the electrons with the field, into a perpendicular component and a component tangent to the surface. But any force on electrons tangent to the surface is going to move them to a different position on the surface, violating the principle that they were already in their minimum energy configuration.

In other words the minimum energy charge configuration will not allow any component of force tangent to the object surface. Therefore the lines of the electric field must be everywhere perpendicular to the surface.

Notice that there is an implicit assumption in my explanation that the electrons in the object are free to move about. This implies that we are talking about a conductor. That same assumption is implicit in the question. on charged surfaces where the charges are not free to move, you may find electric field lines not perpendicular to the surface.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.