Predict a charged particle’s path between plates
You will be able to: Combine uniform electric acceleration with independent motion components.
Why does horizontal entry create a curved path?
A charged bead enters a uniform upward electric field moving horizontally. The field changes its vertical velocity while its horizontal velocity stays constant if no horizontal force acts. This resembles projectile motion, but the charge sign can reverse the acceleration.
A useful starting point: Dielectrics: what stays fixed matters →
Words and symbols before equations
- Acceleration a
- Change of velocity per second; a=qE/m for the electric force alone.
- Uniform field
- Constant magnitude and direction, approximately between large plates away from edges.
- Initial velocity
- Velocity when the particle enters the modeled region.
- Independent components
- Solve x and y motion with their own initial conditions and accelerations.
What this picture assumes
Enlarged bead model: m=0.002 kg, upward E=1000 N/C, v_x=1 m/s, y₀=0, v_y0=0. Plates at y=±0.10 m; uniform region spans x=0–0.50 m. Gravity and edge effects ignored. All allowed settings remain inside the gap; axes in m use equal spatial scale.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- t=0.2 s: x=0.2 m, y=0.02 m, v_y=0.2 m/s. a_y=1 m/s²; horizontal speed stays 1 m/s. Both axes use 900 drawing units/m.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Take +x right and +y up. If E points up, positive q gives upward acceleration and negative q gives downward acceleration. The force direction follows qE, not the particle’s current velocity.
For initial horizontal speed v_x and zero vertical speed, x=v_x t and y=(1/2)(qE/m)t². Eliminating time produces a parabola. The electric field need not bend the trajectory along field lines.
Use these equations only while the particle remains in the uniform region. A plate collision or exit ends that model. The explorer deliberately uses an enlarged charged-bead model and neglects gravity and edge fields; it is not a realistic electron gun.
A worked example, step by step
A bead has q=+2 μC, m=0.002 kg and horizontal speed 1 m/s in upward E=1000 N/C. Find its displacement after 0.20 s.
- a_y=qE/m=(2×10⁻⁶)(1000)/0.002=1 m/s² upward.
- x=v_x t=1(0.20)=0.20 m.
- y=0.5(1)(0.20)²=0.020 m; v_y=a_y t=0.20 m/s.
- The horizontal speed stays 1 m/s while vertical speed increases.
Acceleration follows qE. A moving negative charge does not necessarily move opposite the field at every instant, even though its electric acceleration does.
Does reversing q reverse the initial horizontal velocity?
Compare with an explanation
No. It reverses electric acceleration; the same entry velocity is retained.
Predict. Change one thing. Explain.
Change the bead’s charge sign and move time forward. Compare the curved position trace with the acceleration direction. Geometry and time ranges keep the path between the plates.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
t=0.2 s: x=0.2 m, y=0.02 m, v_y=0.2 m/s. a_y=1 m/s²; horizontal speed stays 1 m/s. Both axes use 900 drawing units/m.
Enlarged bead model: m=0.002 kg, upward E=1000 N/C, v_x=1 m/s, y₀=0, v_y0=0. Plates at y=±0.10 m; uniform region spans x=0–0.50 m. Gravity and edge effects ignored. All allowed settings remain inside the gap; axes in m use equal spatial scale.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant charge, field or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA bead enters horizontally at 2 m/s with a_y=−2 m/s² and v_y0=0. After 0.10 s, (a) find x, (b) find y−y₀, (c) find v_y, and (d) state the field-region condition.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: x=0.20 m.
- 1 point: Δy=−0.010 m.
- 1 point: v_y=−0.20 m/s.
- 1 point: The particle must remain in the uniform-field region without striking a plate.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What sets electric acceleration?
Signed qE/m.
RECALL 2Why a parabola for horizontal entry?
x grows linearly with time while y changes quadratically.
RECALL 3When must the calculation stop?
At a plate collision or exit from the modeled field region.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Predict a charged particle’s path between plates
- a_y=qE_y/m.
- x=v_x t; y=y₀+v_y0 t+(1/2)a_y t².
- Stop the model at a plate boundary or region exit.
Remember: Acceleration follows qE. A moving negative charge does not necessarily move opposite the field at every instant, even though its electric acceleration does.
Conditions: Enlarged bead model: m=0.002 kg, upward E=1000 N/C, v_x=1 m/s, y₀=0, v_y0=0. Plates at y=±0.10 m; uniform region spans x=0–0.50 m. Gravity and edge effects ignored. All allowed settings remain inside the gap; axes in m use equal spatial scale.
Refresh Kid · AP Physics 2 Unit 2 (official Unit 10) · Objectives 10.6.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.6, objectives 10.6.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the second AP Physics 2 unit; College Board numbers it Unit 10; the first unit in this course is official Unit 9. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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