# 7.4.4 Uniform Electric Field

### Uniform Electric Field Strength

• The magnitude of the electric field strength in a uniform field between two charged parallel plates is defined as: • Where:
• E = electric field strength (V m-1)
• V = potential difference between the plates (V)
• d = separation between the plates (m)

• Note: the electric field strength is now also defined by the units V m-1
• 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

• Remember this equation cannot be used to find the electric field strength around a point charge (since this would be a radial field)
• The direction of the electric field is from the plate connected to the positive terminal of the cell to the plate connected to the negative terminal The E field strength between two charged parallel plates is the ratio of the potential difference and separation of the plates

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

#### Worked Example

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

Calculate the electric force acting on a stationary charged particle between the plates that has a charge of 2.6 × 10-15 C.

Step 1: Write down the known values

• Potential difference, V = 7.9 kV = 7.9 × 103 V
• Distance between plates, d = 3.5 cm = 3.5 × 10-2 m
• Charge, Q = 2.6 × 10-15 C

Step 2: Calculate the electric field strength between the parallel plates  Step 3: Write out the equation for electric force on a charged particle

F = QE

Step 4: Substitute electric field strength and charge into electric force equation

F = QE = (2.6 × 10-15) × (2.257 × 105) = 5.87 × 10-10 N = 5.9 × 10-10 N (2 s.f.)

#### Exam Tip

Remember the equation for electric field strength with V and d is only used for parallel plates, and not for point charges (where you would use E = F/Q)

### 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 ΔV across them create a uniform electric field
• The electric field strength between the plates is given by the equations: • Rearranging the fractions by multiplying by Q and d on both sides, gives:

Fd = ΔVQ

• When a charge Q moves from one plate to the other, its work done is

W = Fd

• Where:
• W = work done (J)
• F = force (N)
• d = distance (m) 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 ΔV between parallel plates is also given by:

W = ΔVQ

#### Worked Example

Calculate the force needed to move an electron between two parallel plates 2 m apart with a potential difference of 400 V between them Close Close

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