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Electric Field Strength
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-1C2m-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 εo is used. The value of εo 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 Coulombís law.  
Thus we have  
   
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