1.6: Electric Field E

The region around a charged body within which it can exert its electrostatic influence may be called an electric field. In principle, it extends to infinity, but in practice it falls off more or less rapidly with distance. We can define the intensity or strength \(E\) of an electric field as follows. Suppose that we place a small test charge \(Q\) in an electric field. This charge will then experience a force. The ratio of the force to the charge is called the intensity of the electric field, or, more usually, simply the electric field. Thus I have used the words “electric field” to mean either the region of space around a charged body, or, quantitatively, to mean its intensity. Usually it is clear from the context which is meant, but, if you wish, you may elect to use the longer phrase “intensity of the electric field” if you want to remove all doubt. The field and the force are in the same direction, and the electric field is a vector quantity, so the definition of the electric field can be written as

\[\textbf{F} = Q\textbf{E} \tag{1.6.1} \label{1.6.1}\]

The SI units of electric field are newtons per coulomb, or N C-1. A little later, however, we shall come across a unit called a volt, and shall learn that an alternative (and more usual) unit for electric field is volts per metre, or V m-1. The dimensions are MLT-2Q-1.

You may have noticed that I supposed that we place a “small” test charge in the field, and you may have wondered why it had to be small, and how small. The problem is that, if we place a large charge in an electric field, this will change the configuration of the electric field and hence frustrate our efforts to measure it accurately. So – it has to be sufficiently small so as not to change the configuration of the field that we are trying to measure. How small is that? Well, it will have to mean infinitesimally small. I hope that is clear! (It is a bit like that pesky particle of negligible mass m that keeps appearing in mechanics problems!)

We now need to calculate the intensity of an electric field in the vicinity of various shapes and sizes of charged bodes, such as rods, discs, spheres, and so on.

• 1.6A: Field of a Point Charge

• 1.6B: Spherical Charge Distributions

• 1.6C: A Long, Charged Rod

• 1.6D: Field on the Axis of and in the Plane of a Charged Ring

• 1.6E: Field on the Axis of a Uniformly Charged Disc

• 1.6F: Field of a Uniformly Charged Infinite Plane Sheet