# Electric field strength

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## 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!!)

**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.

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 e_{0}, the permittivity of a vacuum, which is almost exactly the same as permittivity for air.

* Example:*.

What's the field strength at a point 2cm from a charge of 2 x 10^{-6}C in air?

( = 9 x 10^{9} mF^{-1})

* Answer:*.