OCR Specification focus:
‘Describe and analyse charged particle motion in a uniform electric field.’
Charged particles experience constant acceleration in a uniform electric field, producing predictable motion essential for understanding devices such as cathode ray tubes and particle accelerators.
Uniform Electric Fields and Charged Particle Motion
A uniform electric field is one in which the field strength has constant magnitude and direction throughout the region. This type of field is commonly created between two large, parallel, oppositely charged plates. A charged particle entering such a field experiences a force that does not vary with position, giving rise to straightforward, analysable motion. According to the OCR specification, students must be able to describe and analyse the motion of charges when subjected to these uniform conditions.
When a charged particle is placed in a uniform electric field, it experiences a force that depends on both the magnitude of the field and the sign of the particle’s charge. This force directly influences its acceleration and subsequent trajectory.
Between oppositely charged, parallel plates, the electric field in the central region is uniform, so a charge experiences a constant force perpendicular to the plates.
Uniform electric field and equipotential lines between parallel plates. Field lines are straight and parallel, and equipotential lines are evenly spaced and perpendicular to the field. Fringing at the plate edges is shown but not required by the syllabus; it does not affect the central uniform region. Source.
EQUATION
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Electric Force (F) = qE
F = Electric force on the particle (newtons, N)
q = Charge of the particle (coulombs, C)
E = Electric field strength (newtons per coulomb, N C⁻¹)
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The sign of the charge determines the direction of the force: a positive charge accelerates in the direction of the electric field, whereas a negative charge accelerates in the opposite direction. This produces distinct patterns of motion used extensively in particle detection and beam steering.
Components of Motion in a Uniform Field
The motion of a charged particle within a uniform electric field can often be broken down into two perpendicular components. This technique becomes particularly useful when the particle enters the field with a non-zero initial velocity.
Motion Parallel to the Electric Field
The component of the particle’s velocity parallel to the electric field is directly influenced by the electric force. The force is constant, so the acceleration remains constant, allowing the motion to be treated using standard kinematics for uniform acceleration.
If the initial velocity parallel to the field is zero: The particle begins from rest and accelerates uniformly.
If the initial velocity is non-zero:
The motion is still uniformly accelerated, but the particle’s initial speed contributes to its overall displacement and final velocity.
The magnitude of the acceleration depends on the charge-to-mass ratio of the particle.
EQUATION
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Acceleration (a) = F / m
a = Acceleration of the particle (metres per second squared, m s⁻²)
F = Electric force (newtons, N)
m = Mass of the particle (kilograms, kg)
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Between these equation blocks, it is important to appreciate that the mass of the particle plays no role in the electric force itself, but it determines how strongly the particle responds to that force.
Motion Perpendicular to the Electric Field
If the particle’s velocity includes a component perpendicular to the electric field, that component remains unaffected by the field, since the field exerts no force in that direction. As a result:
The perpendicular component of velocity remains constant.
The parallel component experiences constant acceleration.
The overall trajectory becomes parabolic, resembling projectile motion in a gravitational field.
This analogy highlights a conceptual symmetry: electric fields influence charged particles in much the same mathematical way that gravitational fields influence masses, except that the sign of the charge affects the direction of acceleration.
Trajectories of Charged Particles
A uniform electric field allows predictable paths to be formed:
Straight-Line Motion
If a particle begins with velocity purely parallel or antiparallel to the electric field, it will undergo linear acceleration or deceleration. The path will remain straight, with speed changing uniformly.
Parabolic Motion
When the particle enters the field with an oblique velocity:
A charged particle entering the uniform field with an initial horizontal velocity experiences a constant vertical acceleration, producing a parabolic trajectory while between the plates.
Diagram of a cathode-ray tube showing the electron gun, focusing/anode electrodes, and electrostatic deflection plates that create a uniform electric field. The field exerts a constant transverse force on the electrons, deflecting the beam while it is between the plates. This apparatus underpins textbook discussions of motion in uniform electric fields. Source.
The horizontal (perpendicular) component stays constant.
The vertical (parallel) component gains or loses speed at a constant rate.
The combined effect produces a smooth curve.
This behaviour is the foundation of electric field deflection systems used in oscilloscopes and older cathode ray displays, where electrons are steered by altering the electric field between plates.
Key Factors Affecting Motion
Several physical quantities play essential roles in determining a charged particle’s motion in a uniform field:
Charge
A larger magnitude of charge produces a greater force for a given field strength, increasing acceleration. The sign dictates the direction.
Mass
For particles with identical charge, lighter particles accelerate more readily. This explains why electrons show dramatic deflection compared with ions in many apparatuses.
Electric Field Strength
A stronger field increases the force on the particle and therefore increases the acceleration.
Initial Velocity
The particle’s entry conditions determine whether the path is straight or parabolic and influence the extent of displacement within the field.
Analysis Techniques
Students should be able to interpret particle trajectories and relate them to the underlying physics. Useful analytical tools include:
Breaking velocity into perpendicular components.
Applying constant acceleration equations to the motion parallel to the field.
Interpreting how changes in field strength or charge alter the curvature of the path.
This structured approach enables clear understanding of how a uniform electric field influences charged particle behaviour and supports deeper study of electric fields in practical and theoretical contexts.
FAQ
The longer the particle remains between the plates, the greater the vertical change in velocity due to constant acceleration.
This means:
A longer field region results in more deflection.
A slower particle (lower initial horizontal speed) also spends more time in the field, increasing curvature.
Both factors shape the steepness of the final trajectory after the particle exits the field.
Reversing the polarity swaps the direction of the electric field, so the direction of the electric force on a charged particle also reverses.
For a positive particle, the deflection changes to the opposite side. For a negative particle, the same applies but in the opposite sense.
The magnitude of the acceleration remains unchanged if the potential difference stays the same.
Inside the uniform field, the particle experiences constant acceleration in one direction and constant velocity in the perpendicular direction, creating a parabolic trajectory.
Once it leaves the field, there is no further electric force acting (assuming no other fields), so the particle continues in a straight line in the direction of its velocity at the exit point.
The main assumption is that edge effects (fringing fields) are negligible. This is valid when the central region of the plates is large compared with the separation.
It is also assumed that the plates are perfectly parallel, the potential difference is stable, and external magnetic or electric fields are absent.
Electrons have a far smaller mass than any ion, giving them a much larger charge-to-mass ratio.
Because acceleration in the field depends on force divided by mass, electrons accelerate far more rapidly than ions, producing noticeably larger curvature in their paths.
Practice Questions
Question 1 (2 marks)
An electron enters a uniform electric field travelling horizontally. Explain why the electron follows a curved path while it is between the plates.
Mark scheme:
Electron experiences a constant electric force in the vertical direction because of the uniform electric field. (1 mark)
Horizontal velocity remains unchanged while vertical velocity increases, producing a curved (parabolic) path. (1 mark)
Question 2 (5 marks)
A positively charged ion enters a region containing a uniform electric field between two parallel plates.
The ion has an initial horizontal velocity and no vertical velocity.
(a) Describe the horizontal and vertical components of the ion’s motion while in the electric field.
(b) Explain how the sign and magnitude of the ion’s charge affect its trajectory.
(c) State what happens to the ion’s motion after it leaves the electric field region.
Mark scheme:
(a)
Horizontal motion: constant speed because no horizontal force acts. (1 mark)
Vertical motion: constant acceleration due to the electric force. (1 mark)
(b)
The ion accelerates in the direction of the electric field because it is positively charged. (1 mark)
A larger charge produces a greater electric force, increasing vertical acceleration and giving a more curved trajectory. (1 mark)
(c)
After leaving the field, the ion travels in a straight line with constant velocity, continuing in the direction of motion at the exit point. (1 mark)
