## A picture to represent a physical law

There would be an extra advantage if one could describe dia-gramatically the physical laws which govern a field. Figure 10.1 may describe which way the wind is blowing or map out the strength of currents in a body of water. It does not give information on the gas laws or on the laws of hydrodynamics. What we need is a picture which not only describes the features of the field but also tells about the physical laws which govern the field and can perhaps be used to predict consequences of these laws.

A representation of electric fields which incorporates the conditions imposed by Coulomb's law is generally credited to Michael Faraday (1791-1867). His idea was slightly different from the representation shown in Figure 10.1, in that he drew

Figure 10.1 A vector field.

hypothetical 'lines of force' instead of vectors. The tangent to the line of force at any point indicated the direction of the field at that point. The density of the lines indicated the strength of the field.

Strong field

Weak field

Faraday's convention represents the strength of the field by the density of the lines of force.

The simplest electric field, that due to a single positive electric charge, is illustrated in Figure 10.2. The lines of force spread out symmetrically. All lines start at the charge, and once we move away from the charge, no lines are created or destroyed. It follows that if we draw an imaginary sphere around the charge, every line of force will cross that sphere. Surprisingly, this simple and obvious observation leads to important physical consequences.

Faraday's convention represents the strength of the field by the density of the lines of force.

Figure 10.2 Electric field due to a single positive point charge.