Electricity is important in several branches of engineering - not only in electrical or electronic engineering. For example the design of the electrostatic precipitator plates for cleaning the solid fuel power stations involves both mechanical engineering (structures and mechanical rapping systems for cleaning the plates) and electrostatics (to determine the electrical forces between solid particles and plates).
The following example and tasks relate to the electrostatic forces between particles. Electric charge is measured in coulombs (C). Charges can be either positive or negative.
The force between two charges
Let and be two charges in free space located at points and . Then will experience a force due to the presence of and directed from towards .
This force is of magnitude where is the distance between and and is a constant.
In vector notation this coulomb force (measured in newtons) can then be expressed as where is a unit vector directed from towards .
The constant is known to be where (farads per metre).
The electric field
A unit charge located at a general point will then experience a force (where is the unit vector directed from towards ) due to a charge located at . This is the electric field newtons per coulomb ( or alternatively ) at due to the presence of .
For several point charges at at etc., the total electric field at is given by
where is the unit vector directed from point towards .
From the definition of a unit vector we see that
where is the vector directed from point towards so that etc., where and are the position vectors of and (see Figure 34).
The work done
The work done (energy expended) in moving a charge through a distance , in a direction given by the unit vector , in an electric field is (defined by)
where is in joules.