4.1 COULOMB'S LAW AND THE SUPERPOSITION PRINCIPLE

The force between two point charges separated by a distance r is proportional to the product of the charges and inversely proportional to the square of their separation. The force on charge q ₁ due to q ₂ in Figure 4.1 is given by

(4.1)

Figure 4.1: Equal and opposite forces between two point charges separated by r-r'.

where is a unit vector that points from q ₁ toward q ₂. The force is attractive or repulsive depending on whether the charges have opposite or like signs, respectively. The force on q ₁ is equal in magnitude and opposite in direction to the force on q ₂ so that F ₁₂ = - F ₂₁ according to Newton's third law. The unit vector may be written as

(4.2)

where q ₁ is located at r and q ₂ is located at r' so that F ₁₂ is

(4.3)

The electric field contribution at r due to charge q ₂ at r' is given by F ₁₂/ q ₁ or

(4.4)

On the CD Color images for many of the figures may be found on the CD-ROM.

In general, we can write that the force acting on a point charge q in an electric field E is given by F = q E. For a collection of point charges