## Coulombs law

Charles Coulomb (1736-1806) is credited with the definitive verification of the hypothesis of Priestley and Cavendish, and showed that the force between two electrically charged spheres varies inversely as the square of the distance separating them. He designed a very sensitive torsion balance which could measure forces as small as 'a ten thousandth part of a grain'.f He established the expression, which bears his name, for the law of force between two stationary electric charges of magnitude q1 and q2:

where k is another universal constant, and q1 and q2 are the two electric charges.

The numerical value of k depends on the units used. If we use the standard units for force and distance, and express the charges q1 and q2 in coulombs, a unit which we will define later, then k has the value k = —^ = 8.99 x 109 N • m2/C2 4pe0

The constant e0 = 8.85 x 10-12 C2/N. m2 is known as the permittivity of free space.

Electric charges exert forces on one another across empty space. We have 'action at a distance', which, just as in the case of gravitation, presents a major puzzle. Again, in the words of Descartes, one might ascribe to electric charges 'knowledge of a truly divine sort of what is taking place at a distance'.

As the wise owl observes, Coulomb's law does not tell the whole story of electric forces. The law applies only when charges are stationary. The set of phenomena associated with charges at

T The grain was conceptually the mass of a grain of wheat, originally defined in France as just over 50 milligrams.

rest forms the subject of electrostatics. A further complication comes into play when charges are moving. This complication turns out to be very important — without it there would be no light, no universe, and we would not exist! It is a central feature of the subject of electrodynamics (Section 10.4).

10.2 'Fields of force' 10.2.1 Vector fields

A representation of gravitational and electrical forces which circumvents some of the conceptual difficulties associated with action at a distance is that each particle of matter and each electrical charge influences the surrounding space, setting up a ''field of force' Matter, simply by its presence, creates a gravitational field, while an electric charge similarly sets up an electric field. These fields spread out continuously from the source in all directions. If a second particle of matter is located in the gravitational field created by the first particle, it experiences a force, and the same is true for a second charge in an electric field. At the same time, gravitational fields have no effect on electric charges, nor are uncharged particles of matter sensitive to electric fields. It is assumed that such fields are present whether or not there is anything there to experience them.

We can define the strength of an electric field (E) as being proportional to the force exerted by the field on a unit positive charge at a given point:

Force is a vector quantity with direction as well as magnitude. Hence gravitational and electric fields are vector fields.

To help us visualise the field, we might draw the field vector at a sample number of points, where the strength of the field could be represented by the length and thickness of the vector. Such a picture is easy to interpret and is often used to describe winds and currents on weather charts.

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