For mathematical simplicity, we will
consider a uniform field (as exists near the centre of the
space between
two parallel, oppositely charged metal plates). 



Consider moving a small positive charge, q, from point A to point B. 

Let the magnitude of the potential difference between points A
and B be ΔV. 

In moving a positive charge from A to B work is done by the
field so the potential at B is less than the potential
at A. 

We will therefore represent the potential difference between A
and B as ΔV. 

Work done, w moving the charge q is given by 



Now, work done per unit charge is
the potential difference, ΔV
and 

force per unit charge is
the electric field strength, E 



Therefore, the relation between potential difference and field
strength is found by simply dividing the above equation by q. 





which is usually written as 



and the term in brackets is called the potential gradient,
as it represents the slope (gradient) of a graph of potential
against distance. 

This equation shows that alternative units for measuring field
strength are Volts per metre, Vm^{1} 

This means that the magnitude of the field strength between the
two parallel plates is simply given by 


