# A-level Physics (Advancing Physics)/Electric Field

Electric field E is the force per. unit charge caused by an electric field:

${\displaystyle E_{electric}={\frac {F_{electric}}{q}}}$

The unit of electric field is NC−1 or Vm−1.In general, the electric field is the rate of change of electric potential (voltage) with respect to distance:

${\displaystyle E_{electric}=-{\frac {dV_{electric}}{dx}}}$

## Special Cases

There are two different types of field which you need to know about. Uniform fields occur between two plates with opposite charges. Here, the electric field is simply:

${\displaystyle E_{electric}={\frac {V_{electric}}{d}}}$

A charged sphere also has an electric field. To gain a formula for this, we divide the formula for force around a charged sphere by q, so:

${\displaystyle E_{electric}={\frac {Q}{4\pi \epsilon _{0}r^{2}}}}$ ,

where ε0 = 8.85 x 10−12C2N−1m−2.

The electric field around a point charge is called a radial field. The field strength is highest at the centre and decreases as the distance from the centre increases. This is reflected in the above formula, which shows that Eelectric is proportional to ${\displaystyle {\frac {1}{r^{2}}}}$ .

## Field Lines

We can represent electric field using field lines. These go from positive charge to negative charge. They are more closely packed together when the electric field is stronger. In a uniform field, they look like the following:

Around two oppositely charged spheres (known as a dipole), they look like the following:

## Questions

1. Two metal plates are connected to a 9V battery with negligible internal resistance. If the plates are 10 cm apart, what is the electric field at either of the plates?

2. What is the electric field at the midpoint between the plates?

3. The charge on an electron is -1.6 x 10−19 C. What is the electric field 1μm from a hydrogen nucleus?

4. What is the direction of this field?

5. A 2C charge is placed 1m from a -1C charge. At what point will the electric field be 0?