Uniform electric field — OCR A-Level Physics
Test yourself on Uniform electric field with OCR A-Level practice questions.
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Uniform electric field explained
A uniform electric field exists between two parallel conducting plates connected to a potential difference V.
Read the full explanation
The field strength E is defined as the force per unit positive charge, and its magnitude is given by E = V/d, where d is the plate separation. The field is directed from the positive plate to the negative plate. For example, if V = 200 V and d = 0.050 m, then E = 200 / 0.050 = 4000 V m⁻¹. The unit V m⁻¹ is equivalent to N C⁻¹. The equation applies only when the field is uniform, which is a good approximation away from the edges of the plates. In this topic you must be able to use E = V/d to calculate field strength, potential difference or separation, and to describe the direction of the field.
(b) parallel plate capacitor; permittivity; C = ε₀A/d; C = εA/d; ε = εrε₀
A parallel plate capacitor consists of two conducting plates separated by a distance d, with area A overlap. Its capacitance C is given by C = ε₀A/d for a vacuum or air, and C = εA/d when a dielectric of permittivity ε is present. The permittivity ε is related to the permittivity of free space ε₀ by ε = εrε₀, where εr is the relative permittivity (dielectric constant) of the material. For example, if A = 0.020 m², d = 1.0 mm = 1.0 × 10⁻³ m, and εr = 2.0, then ε = 2.0 × 8.85 × 10⁻¹² = 1.77 × 10⁻¹¹ F m⁻¹, and C = (1.77 × 10⁻¹¹ × 0.020) / (1.0 × 10⁻³) = 3.54 × 10⁻¹⁰ F. You must be able to use these equations and explain how area, separation and dielectric affect capacitance.
(c) motion of charged particles in a uniform electric field.
When a charged particle enters a uniform electric field, it experiences a constant electric force F = qE. This force causes acceleration a = F/m = qE/m. If the particle enters perpendicular to the field, its motion is analogous to projectile motion: constant velocity parallel to the plates and constant acceleration perpendicular to them. For example, an electron entering midway between two horizontal plates with speed v horizontally will follow a parabolic path, deflecting towards the positive plate. If it enters parallel to the field, it accelerates in a straight line. You must be able to describe the path, calculate acceleration, time of flight, deflection and final velocity components, and explain how the motion depends on charge, mass, field strength and initial velocity.
Your focus
- Define electric field strength as force per unit positive charge.
- Apply E = V/d to solve problems involving uniform fields.
- Describe the direction of a uniform electric field between charged plates.
Show all 9 objectives
- Use C = ε₀A/d and C = εA/d to solve problems.
- Define permittivity and relative permittivity and relate them by ε = εrε₀.
- Explain how plate area, separation and dielectric material affect capacitance.
- Describe the motion of a charged particle in a uniform electric field.
- Calculate acceleration, time of flight and deflection using F = qE and suvat equations.
- Explain how the path depends on initial velocity and field direction.
Uniform electric field exam tips
Marking Points
- State that electric field strength is force per unit positive charge.
- Use E = V/d to calculate E, V or d correctly.
- Recognise that the field between parallel plates is uniform except near the edges.
- State that the field direction is from the positive plate to the negative plate.
- Use the unit V m⁻¹ or N C⁻¹ for electric field strength.
- State the equation for capacitance of a parallel plate capacitor: C = ε₀A/d or C = εA/d.
- Define permittivity and relative permittivity, and use ε = εrε₀.
- Explain that capacitance increases with plate area and permittivity, and decreases with separation.
- Calculate capacitance, area, separation or permittivity using the equations.
- Recognise that ε₀ is the permittivity of free space and εr is dimensionless.
- State that the electric force on a charged particle is F = qE and is constant in a uniform field.
- Use Newton's second law to find acceleration: a = qE/m.
- Describe the path as parabolic when the initial velocity is perpendicular to the field.
- Calculate time of flight from the horizontal velocity and plate length.
- Calculate vertical deflection using suvat equations with acceleration a = qE/m.
- Explain that the motion is independent of the sign of the charge except for the direction of deflection.
Examiner Tips
- 💡Always convert distances to metres before using E = V/d.
- 💡Check that the calculated field direction matches the plate polarity.
- 💡Remember that V m⁻¹ and N C⁻¹ are equivalent units for electric field strength.
- 💡Write down the equation and rearrange before substituting numbers.
- 💡Check that all quantities are in SI units: area in m², separation in m, permittivity in F m⁻¹.
- 💡Remember that adding a dielectric increases capacitance by a factor of εr.
- 💡Draw a clear diagram showing the field direction, initial velocity and expected path.
- 💡Use suvat equations separately for the direction parallel to the field and perpendicular to it.
- 💡Remember that the electric force does not depend on the particle's speed.
Common Mistakes
- Confusing electric field strength with electric potential; correction: field strength is force per unit charge, while potential is work done per unit charge.
- Using E = V/d when the field is not uniform; correction: this equation applies only to a uniform field, such as between parallel plates away from the edges.
- Forgetting that d must be in metres; correction: convert all lengths to metres before calculation.
- Reversing the field direction; correction: the field points from the positive plate to the negative plate.
- Using the diameter instead of the area of the plates; correction: calculate area from the radius if given diameter, and ensure consistent units.
- Forgetting to convert separation to metres; correction: convert mm or cm to m before substitution.
- Confusing ε and ε₀; correction: ε is the permittivity of the dielectric, ε₀ is the permittivity of free space, and ε = εrε₀.
- Assuming εr has units; correction: relative permittivity is a dimensionless ratio.
- Treating the electric force as varying; correction: in a uniform field the force is constant, so acceleration is constant.
- Forgetting to use the correct mass and charge of the particle; correction: use the specific values for an electron, proton, etc., as given.
- Mixing up the directions of velocity and acceleration; correction: resolve motion into components parallel and perpendicular to the field.
- Assuming the particle moves in a circle; correction: in a uniform electric field the path is parabolic (if entering perpendicular) or straight (if parallel).