Uniform Electric Field | AQA A Level Physics Revision Notes 2017

Uniform Electric Field Strength

The magnitude of the electric field strength in a uniform field between two charged parallel plates is defined as:

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

Where:
- E = electric field strength (V m⁻¹)
- V = potential difference between the plates (V)
- d = separation between the plates (m)

Note: both units for electric field strength, V m⁻¹ and N C⁻¹, are equivalent
The equation shows:
- The greater the voltage between the plates, the stronger the field
- The greater the separation between the plates, the weaker the field

This equation cannot be used to find the electric field strength around a point charge
- This is because the field around a point charge is radial

The electric field between two plates is directed:
- From the positive plate (i.e. the one connected to the positive terminal)
- To the negative plate (i.e. the one connected to the negative terminal)

Uniform Electric Field Between two Parallel Plates

Electric field between two plates, downloadable AS & A Level Physics revision notes

The electric field strength between two charged parallel plates is the ratio of the potential difference and separation of the plates

Worked example

Two parallel metal plates separated by 3.5 cm have a potential difference of 7.9 kV between them.

Calculate the electric force acting on a point charge of 2.6 × 10⁻¹⁵ C when placed between the plates.

Answer:

Step 1: List the known quantities

Potential difference between plates, V = 7.9 kV = 7900 V
Distance between plates, d = 3.5 cm = 0.035 m
Charge, Q = 2.6 × 10⁻¹⁵ C

Step 2: Equate the equations for electric field strength

E field between parallel plates: $E = \frac{V}{d}$

E field on a point charge: $E = \frac{F}{Q}$

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

Step 3: Rearrange the expression for electric force F

$F = \frac{Q V}{d}$

Step 4: Substitute values to calculate the force on the point charge

$F = \frac{(2.6 \times 10^{- 15}) \times 7900}{0.035} = 5.9 \times 10^{- 10}$ N (2 s.f.)

Examiner Tip

Remember the equation for electric field strength with V and d is only valid for parallel plates, and not for point charges

However, when a point charge moves between two parallel plates, the two equations for electric field strength can be equated:

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

Top tip: if one of the parallel plates is earthed, it has a voltage of 0 V

Derivation of Electric Field Strength Between Plates

When two points in an electric field have a different potential, there is a potential difference between them
- To move a charge across that potential difference, work needs to be done
- Two parallel plates with a potential difference V across them create a uniform electric field
The electric field strength between the plates is given by the equations:

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

Rearranging the fractions by multiplying by Q and d on both sides, gives:

$F d = V Q$

When a charge Q moves from one plate to the other, the work done on the charge by the field is

$W = F d$

Where:
- W = work done on charge (J)
- F = electrostatic force (N)
- d = distance between plates (m)

Parallel Plates Work Done, downloadable AS & A Level Physics revision notes

The work done on the charge depends on the electric force and the distance between the plates

Therefore, the work done in moving a charge Q through a potential difference V between parallel plates is also given by:

$W = Q V$

Worked example

Calculate the electrostatic force on an electron between two parallel plates 20 cm apart and have a potential difference of 400 V applied between them.

Answer:

Step 1: List the known quantities

Potential difference, V = 400 V
Distance between plates, d = 20 cm = 0.2 m
Charge of an electron, Q = 1.60 × 10⁻¹⁹ C

Step 2: Write an expression for the electrostatic force between two parallel plates

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

$F = \frac{Q V}{d}$

Step 3: Substitute the values into the expression

$F = \frac{400 \times (1.60 \times 10^{- 19})}{0.2} = 3.2 \times 10^{- 16}$ N

Uniform Electric Field (AQA A Level Physics)

Revision Note

Uniform Electric Field Strength

Uniform Electric Field Between two Parallel Plates

Worked example

Examiner Tip

Derivation of Electric Field Strength Between Plates

Worked example

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Katie M