The Force Acting
Between Two Electric Charges: Coulomb's Law 

The force between two charges is directly
proportional to their magnitudes and inversely proportional
to the square of the distance between them. 



Mathematically, we write this as 



and putting the two statements together we have 



The value of constant depends on the medium in which the charges are situated 



For reasons of standardization of physics formulae*, the
constant is written in a slightly surprising way. 

It is written as 



where ε is the
constant which characterizes the medium. It is called the
permittivity of the medium. 

Thus we have 



By considering the units of the other quantities in
the above equation we see that the units of permittivity must be N^{1}C^{2}m^{2} 

However, this combination of units is usually
written as Farads per metre, Fm^{1} (where
1F = 1VC^{1}) 

If the "medium" is a vacuum, then the symbol
ε_{o} is used. The value
of ε_{o} is 8.85×10^{12}
Fm^{1} 



* It was agreed that equations describing situations
where there is spherical symmetry, as in this case, would (where
possible) have the term 4π in
them. Similarly if there is cylindrical symmetry, 2π
appears. 



Relative Permittivity
(or Dielectric Constant) 

The permittivity of a material is always greater
than the permittivity of empty space. 

The relative permittivity of a material is the ratio
of its absolute permittivity to the permittivity of empty space 



and this is, of course, a number without units
(being a ratio of two quantities having the same units). 



Electric Field Strength, E 

The electric field strength at
a point in an electric field is the force per unit charge
acting on a small positive test charge placed at that
point. 

(You might see a slightly different definition: "the
force acting on a unit positive charge". It comes down to the
same thing, of course, but the above definition tries to be a little
more "practical"... the basic unit of charge, the Coulomb, is a
very big quantity of charge.) 



As an equation, this definition is 



The units of E
are therefore NC^{1} and the sense of E is
defined to be that of the force on a positive charge (as
stated in the definition). The "+" is added to the equation here as
a reminder of that fact but is usually missed out. 

It should be clear from the definition that
E is a vector quantity. 



Electric Field Strength at a Distance r from
a Point Charge of Magnitude, Q 



To calculate the field strength
at point p, imagine a 1C
(positive) charge to be placed at p and then use Coulomb’s law. 

Thus we have 


