Physics • Year 12 • Module 6: Electromagnetism • Lesson 2
Trajectories in Electric Fields
Lock in the core vocabulary, the SUVAT equations for charged-particle motion, and the direction rules for parabolic trajectories before tackling calculations.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: trajectory, parabolic path, time of flight, electric acceleration, deflection, independence of motion, uniform electric field, horizontal velocity, vertical velocity component, impact velocity. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The complete path followed by a particle through space as a function of time. | |
| 1.2 | The curved path traced by a particle under a constant perpendicular force; the same shape as a projectile under gravity. | |
| 1.3 | The duration a charged particle spends inside the region between two charged plates. | |
| 1.4 | The constant acceleration given by a = qE/m produced on a charged particle in a uniform electric field. | |
| 1.5 | The perpendicular displacement of a particle from its original straight-line path due to a transverse electric force. | |
| 1.6 | The principle that the horizontal and vertical motions of a particle in a field do not affect each other. | |
| 1.7 | An electric field that has the same magnitude and direction at every point, produced between two large parallel plates. | |
| 1.8 | The component of a particle's velocity parallel to the plates, which remains constant throughout the motion. | |
| 1.9 | The component of a particle's velocity perpendicular to the plates, which increases uniformly due to the electric force. | |
| 1.10 | The resultant speed and direction of a particle at the moment it exits the electric field region. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 A charged particle entering a uniform electric field perpendicular to the field lines follows a circular path. T / F
2.2 The horizontal component of a charged particle's velocity remains constant as it moves between parallel plates (ignoring gravity). T / F
2.3 An electron and a proton fired horizontally into the same electric field will both curve in the same direction. T / F
2.4 The time of flight between plates is calculated using t = L / vx, where L is the plate length and vx is the horizontal speed. T / F
2.5 The vertical deflection of a charged particle between plates is independent of the particle's mass. T / F
2.6 Increasing the horizontal launch speed of a particle increases its time of flight between plates of fixed length. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
parabola · horizontal · constant · qE/m · perpendicular · charge · opposite · increases
When a charged particle enters a uniform electric field at right angles to the field lines, the electric force acts ___________ to its initial velocity. Because this force is constant, the particle traces a ___________ — exactly like a projectile in gravity. The ___________ component of velocity is unchanged throughout the motion, while the vertical speed ___________ uniformly due to the constant electric acceleration. This acceleration is given by ___________, and its direction depends on the sign of the particle's ___________. An electron curves in the ___________ direction to a proton in the same field, because the two particles carry opposite signs of charge. The ___________ nature of horizontal motion means t = L/vx gives the time of flight.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 State the two SUVAT equations used to find the vertical deflection and vertical exit speed of a charged particle between plates.
4.2 Why does the trajectory of a charged particle in a uniform electric field have the same mathematical form as projectile motion under gravity?
4.3 How do you determine whether a charged particle will strike a plate before exiting the field?
4.4 Explain why increasing the horizontal launch speed of an electron reduces its deflection between plates of fixed length.
5. Formula identification & variable naming
For each formula below, name the quantity each symbol represents and state its SI unit. 12 marks (1 per cell)
| Formula | What it calculates | Key variable and unit |
|---|---|---|
| t = L / vx | ||
| a = qE / m | ||
| y = ½at² | ||
| vy = at | ||
| v = √(vx² + vy²) | ||
| θ = tan−1(vy / vx) |
Q1 — Term–definition match
1.1 trajectory • 1.2 parabolic path • 1.3 time of flight • 1.4 electric acceleration • 1.5 deflection • 1.6 independence of motion • 1.7 uniform electric field • 1.8 horizontal velocity • 1.9 vertical velocity component • 1.10 impact velocity.
Q2 — True / false with correction
2.1 False. A charged particle entering a uniform field with velocity perpendicular to the field follows a parabolic path, not a circular one. A circular path requires a force that always points toward the centre, which is not the case for a uniform field.
2.2 True. No horizontal force acts (ignoring gravity), so vx remains constant throughout.
2.3 False. An electron and a proton curve in opposite directions because they carry opposite signs of charge. In a downward E-field, the force on a positive proton is downward (F = qE) but the force on a negative electron is upward.
2.4 True. Horizontal motion is uniform, so t = L / vx applies directly.
2.5 False. The deflection y = ½at² = ½(qE/m)t² depends on the charge-to-mass ratio q/m. A more massive particle with the same charge has a smaller acceleration and therefore smaller deflection.
2.6 False. A higher horizontal speed means the particle crosses the same plate length L in less time (t = L/vx), so the time of flight decreases.
Q3 — Cloze paragraph
In order: perpendicular / parabola / horizontal / increases / qE/m / charge / opposite / constant.
Q4.1 — SUVAT equations for vertical motion
Vertical deflection: y = uyt + ½at² (for a horizontal entry, uy = 0, so y = ½at²). Vertical exit speed: vy = uy + at (simplifies to vy = at for horizontal entry). Here a = qE/m.
Q4.2 — Why the same form as projectile motion
In projectile motion, gravity provides a constant downward force on the mass (F = mg), giving a constant acceleration g. In a uniform electric field, the electric force F = qE is also constant in magnitude and direction, giving constant acceleration a = qE/m. Because both situations involve a constant transverse force with no force along the initial velocity direction, the mathematics (and therefore the shape of the trajectory) is identical.
Q4.3 — Condition for striking a plate
Calculate the deflection y = ½at² at time t = L/vx. If the magnitude |y| exceeds half the plate separation (d/2), the particle strikes the plate before exiting. If |y| ≤ d/2, the particle exits the field without hitting a plate.
Q4.4 — Higher horizontal speed reduces deflection
A higher horizontal speed vx means the particle spends less time between the plates: t = L/vx decreases. Since vertical deflection is y = ½at² and a is unchanged, a shorter time t gives a much smaller y (deflection scales as t²). The electric force has less time to act, so the particle is deflected less.
Q5 — Formula identification
t = L/vx: Time of flight between the plates (s); L = plate length (m), vx = horizontal speed (m/s).
a = qE/m: Electric acceleration of the particle (m/s²); q = charge (C), E = field strength (V/m), m = mass (kg).
y = ½at²: Vertical deflection from the entry path (m); a = electric acceleration (m/s²), t = time of flight (s).
vy = at: Vertical speed at exit (m/s); a = electric acceleration (m/s²), t = time of flight (s).
v = √(vx² + vy²): Resultant (impact) speed at exit (m/s); vx and vy are horizontal and vertical components respectively.
θ = tan−1(vy/vx): Angle of exit velocity above/below the horizontal (°); vy and vx are the two velocity components at exit.