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Uniform electric fields and field strength

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What an electric field is

An electric field is a region in which a charge experiences a force.
It is a vector — it has a direction at every point.
The direction of the field is defined as the direction of the force on a positive charge.
- So field lines point away from positive charges and toward negative ones.

The uniform field between parallel plates

Two flat parallel plates connected to a power supply produce a uniform field in the gap between them.
Uniform means the field has the same strength and the same direction at every point in the gap.
On a diagram it is drawn as evenly spaced parallel field lines, running from the positive plate to the negative plate.
- Even spacing is what shows the field is uniform — lines that fan out or bunch up would mean a changing strength.
- The lines are always perpendicular to the plates.
At Level 2 you only deal with the uniform field. The field of a single point charge, which weakens with distance, is Level 3.

Electric field strength

$E = \frac{V}{d}$

$E$ — electric field strength (V m⁻¹, which is the same unit as N C⁻¹)
$V$ — the voltage (potential difference) between the plates (V)
$d$ — the separation of the plates (m)
The two units are genuinely equivalent: field strength is both "volts per metre of gap" and "newtons of force per coulomb of charge".
The relationship says:
- more voltage across the same gap → stronger field,
- a wider gap at the same voltage → weaker field, because the same potential difference is spread over more distance.
$d$ is the plate separation, not the distance the charge has moved and not the length of the plates.

Drag the charge around the gap below. The field lines stay evenly spaced and parallel, so the force is the same size and direction wherever you put it — that is what uniform means. Change the voltage or the plate spacing and watch $E = V/d$ respond:

Voltage V = 200 V

Separation d = 4 cm

Charge q = 2 µC

E = V/d = 200/0.04 = 5,000 V/m

F = qE = 10.00 mN (same everywhere)

What changes the field and what does not

Change	Effect on $E$
Double the voltage	Doubles
Double the plate separation	Halves
Move the charge to a different point in the gap	No change — the field is uniform
Use a bigger charge	No change — $E$ depends only on the plates

This last row matters: the field is a property of the plates, not of whatever you put between them. The charge only comes in when you calculate the force on it.

Worked ExampleField strength between plates

Two parallel plates are $4.0$ mm apart with a potential difference of $200$ V across them. Find the electric field strength between them, and state its direction.

Step 1 — Convert the separation to metres

$d = 4.0 \text{ mm} = 4.0 \times 10^{-3} \text{ m}$

Step 2 — Apply the field relationship

$E = \frac{V}{d} = \frac{200}{4.0 \times 10^{-3}} = 5.0 \times 10^{4} \text{ N C}^{-1}$

Step 3 — Direction

The field points from the positive plate toward the negative plate, perpendicular to both.

$E = 5.0 \times 10^{4} \text{ N C}^{-1} \text{, from the positive plate to the negative plate}$

Worked ExampleWorking back to a plate separation

A uniform field of strength $2.5 \times 10^{4}$ V m⁻¹ is required between two plates connected to a $150$ V supply. How far apart must the plates be?

Step 1 — Rearrange

$E = \frac{V}{d} \;\Rightarrow\; d = \frac{V}{E}$

Step 2 — Substitute

$d = \frac{150}{2.5 \times 10^{4}} = 6.0 \times 10^{-3} \text{ m} = 6.0 \text{ mm}$

$d = 6.0 \text{ mm}$