18.2.2Electric fields and capacitance (A Level)
Motion of Charged Particles
5 min read 9 parts Lesson 6 of 19 1 quiz
Lesson summary
18.2.2 Motion of Charged Particles — AS PHYSICS 9702 notes: Describe and calculate the motion of charged particles in a uniform electric field.Force — F = QE, constant in size and direction in a uniform fieldAcceleration — a = QE/m, in the direction of the forceEquations of motio…
- Equations of motion
- Neutral particle
- Starting from rest
- Independent of path
- Initial speed u along or against the field
- Parallel to the plates
Section 1 of 9Constant force and acceleration
Constant force and acceleration
Force
- F = QE, constant in size and direction in a uniform field
Acceleration
- Acceleration a = QE/m, in the direction of the force
Equations of motion
- Equations of motion the constant-acceleration (suvat) equations apply along the field
Gravity
- Gravity ignored for electrons and ions as it is tiny compared with the electric force, but included for a heavy charged oil drop
Neutral particle
- Neutral particle an uncharged particle such as a neutron feels no force and passes straight through
Section 2 of 9Acceleration along the field
1Starting from rest
- Starting from rest the work done by the field is QV, which becomes kinetic energy, ½mv² = QV, so v = √(2QV/m)
2Use
- Use an electron gun accelerates electrons through a few kilovolts
3Independent of path
- Independent of path the result depends only on V
4Initial speed u along or against the field
- Initial speed u along or against the field v² = u² ± 2as with a = QE/m
- If the force opposes the velocity the particle decelerates, may stop and then reverse
Section 3 of 9Motion at right angles to the field
1Path
- Path a particle entering perpendicular to the field follows a parabola, like a projectile in gravity
2Parallel to the plates
- Parallel to the plates no force, so the velocity is constant, x = vx t
3Perpendicular to the plates
- Perpendicular to the plates constant force from zero initial speed, y = ½at² and vy = at with a = QE/m
4Time between plates of length L
- Time between plates of length L t = L/vx
5Leaving the field
- Leaving the field the deflection angle satisfies tan θ = vy/vx, and outside the plates the path is straight
6Direction of bending
- Direction of bending a positive charge bends towards the negative plate and a negative charge towards the positive plate
Section 4 of 9Comparing particles
Comparing particles
Deflection depends on
- Deflection depends on charge, mass (more mass, less deflection) and speed (more speed, less deflection)
- (more charge, more deflection)
Charge-to-mass ratio
- Charge-to-mass ratio particles with larger Q/m are deflected more
Electron and proton
- Electron and proton the electron has a Q/m about 1800 times larger, so it is deflected far more
Applications
- Applications cathode-ray oscilloscope and separation of particles with different Q/m
Magnetic fields
- Magnetic fields the force is perpendicular to the velocity, giving circular rather than parabolic paths
Section 5 of 9Projectile analogy
Gravity analogy
- Gravity analogy a ball thrown horizontally has constant horizontal velocity and constant vertical acceleration g
Replace g by QE/m
- Replace g by QE/m y = ½(QE/m)t², and eliminating t gives y = (QE/2mv_x²)x²
Deflection limit
- Deflection limit if the deflection exceeds half the plate separation the particle hits a plate
Section 6 of 9Strategy
1
Draw the field direction and find the force direction from the sign of the charge
2
Find a = QE/m, or QV/(md)
3
Split the motion into components parallel and perpendicular to the field
4
Use suvat along the field and constant velocity across it, with time linking them
Exam answers
- Exam answers state the force direction, then the acceleration, then the time in the field, then the deflection
Assumptions
- Assumptions state that edge effects and gravity are ignored and that the field is uniform only between the plates
Section 7 of 9More from the specification
More from the specification
Uniform electric field between plates
- Two parallel plates connected to high-voltage terminals with potential difference V separated by distance d set up a uniform electric field of strength E = V / d, represented by parallel, equally spaced field lines.
Electric force on charged particles
- The magnitude of the electric force on a charged particle of charge q is FE = qE, acting parallel to electric field lines for positive charges and vice versa for negative electrons.
Parabolic trajectory in electric fields
- When a charged particle or nucleus enters a perpendicular uniform electric field, it undergoes constant transverse acceleration a = qE / m while maintaining constant horizontal velocity, following a parabolic path.
- (such as a proton or boron nucleus)
Deflection comparison between particles
- For particles entering with equal velocity, acceleration and deflection depend on charge-to-mass ratio (q / m);
- a boron nucleus (11_5 B3+) has a smaller q/m ratio than a proton (1_1 p^+) and thus deflects less.
Uniform electric field between plates
- Two parallel plates connected to high-voltage terminals with potential difference V separated by distance d set up a uniform electric field of strength E = V / d, represented by parallel, equally spaced field lines.
Electric force on charged particles
- The magnitude of the electric force on a charged particle of charge q is FE = qE, acting parallel to electric field lines for positive charges and vice versa for negative electrons.
Parabolic trajectory in electric fields
- When a charged particle or nucleus enters a perpendicular uniform electric field, it undergoes constant transverse acceleration a = qE / m while maintaining constant horizontal velocity, following a parabolic path.
- (such as a proton or boron nucleus)
Deflection comparison between particles
- For particles entering with equal velocity, acceleration and deflection depend on charge-to-mass ratio (q / m);
- a boron nucleus (11_5 B3+) has a smaller q/m ratio than a proton (1_1 p^+) and thus deflects less.
Trajectory
- The path followed by a projectile, a parabola.
Field strength
- G = Fg/m.
Potential difference
- Work done by a unit charge passing through a component.
Field lines
- Lines showing the direction and strength of a magnetic field.
Nucleus
- Small, dense, positively charged centre of the atom.
Distance
- Total length of path travelled, a scalar.
Terminal
- Connection point of a cell, labelled + or −.
Stationary
- Not moving.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Uniform field | a field of constant magnitude and direction |
| Charge-to-mass ratio | Q/m, which determines the acceleration in a given field |
| Parabolic path | the trajectory of a charge entering perpendicular to a uniform field |
| Deflection | the sideways displacement caused by the field |
| Electron gun | a device that accelerates electrons through a p.d. |
| Projectile motion | motion with constant velocity in one direction and constant acceleration in the other |
Section 9 of 9Exam technique
1
Applying constant acceleration along the plates — the velocity parallel to the plates is constant.
2
Deflecting a negative charge towards the negative plate — it moves towards the positive plate.
3
Ignoring Q/m — deflection depends on charge and mass together.
4
Forgetting the straight path after leaving the plates — no force acts outside the field.
Marked practiceQuizzes for this lesson
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).