2 Engineering Example 1
2.1 Electrostatic potential
Introduction
The electrostatic potential due to a point charge [maths rendering] coulombs at a position [maths rendering] (m) from the charge is given by
[maths rendering]
where [maths rendering] , the permittivity of free space, [maths rendering] and [maths rendering] .
The field strength at position [maths rendering] is given by [maths rendering] .
Problem in words
Find the electric field strength at a distance of 5 m from a source with a charge of 1 coulomb.
Mathematical statement of the problem
[maths rendering]
Substitute for [maths rendering] and [maths rendering] and use [maths rendering] , so that
[maths rendering]
We need to differentiate [maths rendering] in order to find the electric field strength from the relationship [maths rendering]
Mathematical analysis
[maths rendering]
When [maths rendering] ,
[maths rendering] ( [maths rendering] .)
Interpretation
The electric field strength is [maths rendering] at [maths rendering] m.
Note that the field potential varies with the reciprocal of distance (i.e. inverse linear law with distance) whereas the field strength obeys an inverse square law with distance.