1 Electric force – Coulomb’s law

A point charge is a hypothetical charged particle that occupies a single point in space. It has no internal structure, motion or spin, so a stationary point charge is only affected by electric fields and not affected by magnetism. It is useful when defining the concept of electric force.

It is important to keep in mind, however, that the electric force is experienced not only by stationary point charges. The electric force is felt by all charges, whether they are moving or not.

Before looking at the electric force in more detail, it is useful to consider forces in general. Unlike charge, force is a vector quantity – it has a magnitude and a direction – and its conventional symbol is . The SI unit of force is the newton (N), where 1 N is equivalent to 1 kg m s.

Newton’s second law of motion states that the force on a particle is equal to its rate of change of momentum or, when the force is applied to a body with a mass that does not change with time, its mass m multiplied by its acceleration . Mathematically this is written as

Equation 1 gives an example of a vector quantity (in this case acceleration) multiplied by a scalar quantity (mass). The result of this operation is another vector (force).

Multiplying a vector by a scalar

If any vector is multiplied by any scalar , the result is another vector . The magnitude of is equal to the scalar factor multiplied by the magnitude of the original vector. You can express this as or .

If the scalar factor is positive then the product will be parallel to the original vector. If the scalar factor is negative then the product will be antiparallel to the original vector (Figure 1).

Also note the following general points, where could represent any vector.

Figure 1 Multiplying a vector by a scalar . Here, the resultant vector is shown for and .

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This figure illustrates the multiplication of a vector E by a scalar q. An orange arrow representing the vector E points to the right. A blue arrow is labelled ‘vector F equals q times vector E, open bracket q greater than zero close bracket’. This blue arrow points in the same direction as vector E. A second blue arrow is labelled ‘vector F equals q times vector E, open bracket q less than zero close bracket’. This blue arrow points in the opposite direction to vector E. The two blue arrows are a different length to the vector E but the same length as each other.

Multiplying a vector by a scalar . Here, the resultant vector is shown for and ....

• The quantity

  Equation label: (2)

  is a vector of magnitude 1 (with no units) pointing in the same direction as . This vector is called the unit vector of and is given the symbol (pronounced F-hat).

• Writing

  Equation label: (3)

  neatly splits a vector into a product of two terms:

  • gives the magnitude of the vector

  • gives its direction in space.

• The units of are contained in the magnitude, . Any unit vector is dimensionless and has magnitude 1; not 1 newton or 1 of anything else.

• Two vectors with the same magnitude and the same direction are defined as being equal, but remember that they can have different starting points.

The study of time-independent (static) electrical phenomena is known as electrostatics. The sections that follow focus on the electric force between static point charges. This so-called electrostatic force between two stationary point charges is given by Coulomb’s law, which has the following observable properties.

If and have the same sign, then Equation 4 predicts . This is interpreted as a repulsive force.