What is an Electric Field

The first fact most students learn about electricity and magnetism is that there exists a physical property known as charge, which can be positive or negative. Two particles of like charge repel one another, and two particles with opposite charges attract one another, with a force proportional to the strength of each charge, and inversely proportional to the square of the distance between the charges.

Instead of talking directly about the electric force, we can instead consider it in terms of electric fields. In this representation, each charged particle is seen as modifying the space around it. A positively charged particle creates an electric field that points away from it, while a negatively charged particle creates an electric field that points toward it. The field gets weaker as the inverse of the distance from the particle squared.

If we drop another “test” particle in this electric field, we can compute the force on it by multiplying the “test” charge by the strength of the electric field at the point where the charge is released, F=qE. If q is positive, the force is in the same direction as the electric field. If q is negative, the force is in the opposite direction. So with a little thought, you can see that like charges will repel one another, and opposite charges will attract each other, as we desire.

Thinking in terms of “fields” instead of “forces” might seem like a small change, but it actually helps you understand what is going on much more easily. To demonstrate, let’s consider two additional facts.

The electric field is zero inside any conductor.

Changes in the electric field propagate at the speed of light.

Let us first consider why #1 is true. Remember that, by definition, a conductor is a material in which electrons are free to move. Electrons have a (negative) charge, so if you try to set up an electric field inside a conductor, the electrons in the material will experience a force and, because they are able to, will move. In fact, they will keep moving until they either run out of conductor to move in, or the electric field, and thus force, falls to zero. In reality, both happen – charges will move onto the surface of the conductor in such a way and in such numbers that they produce their own electric field inside the conductor that exactly cancels the electric field you set up. This doesn’t happen instantly, so, in truth, an electric field can exist inside a conductor, but (at least if the field you set up is unchanging), not for long.

This principle has some practical uses. In general, any time you place an object inside a hollow conductor to protect it from electric fields, we say the conductor is a “Faraday cage.” Your car acts as a Faraday cage if it is struck by lightning. With the right amount of paranoia, you could make a Faraday cage wallet.

Now let’s consider point #2. Suppose I have two charges. The first charge creates an electric field in space, and the second charge feels a force F=qE because of that electric field. Now suppose I move the first charge. Does the force on the second charge change right away? No, it doesn’t, because changes in the electric field only propagate at the speed of light.

If it seems odd to you that it should be the speed of light and not some other speed, know that light itself is nothing but an electromagnetic wave – a wave made up of electric and magnetic fields. In the 19th century, James Clerk Maxwell wrote down equations that now bear his name that related charge, and changes in the magnetic field, to the electric field, along with similar equations for the magnetic field. He found that these equations actually predicted the existence of electromagnetic waves traveling at what had been previously measured as the speed of light. In 1887, Heinrich Hertz first intentionally generated and detected electromagnetic waves using an electronic device.

To learn more about the electric field, a concept much too big to cover in a Helium article, pick up any physics textbook.