Electric field strength

This is defined as the force per unit charge acting at a point in the field. So an equation for it is:

Where:.

E = electric field strength

F = force acting in newtons

q = the charge in coulombs

Units of E: NC^-1 or Vm^-1 (these are the same thing!!)

Uniform Fields

There is one special example you also need to know:

This is a uniform field. The field strength at any point in this field is:

where.

V = the pd between the plates

d = the distance separating the plates.

Field strength is a vector - it has direction as well as magnitude.

This is important to remember because in electric fields you can have field strengths acting in different directions due to different signs of charge.

Radial Fields

A particularly useful equation to find field strength around a point charge (note - the first pictures is the field diagram section were point charges) is:

where.

Q = the charge causing the field

r = the separation between the charge and the point you are considering

ε = permittivity (see below for notes).

You can also write this as

This shows that:

E ∝ Q - the bigger the charge, the stronger field.
E ∝ - another inverse square relationship. The further you are from the charge, the weaker the field strength.
The constant of proportionality is . Now this number varies depending on what the field is in. An electric field in water has different properties to a field in a vacuum, for example. So for each medium, you need a value of e, the permittivity. The one used most commonly at A-level is e₀, the permittivity of a vacuum, which is almost exactly the same as permittivity for air.