A moving charge produces a magnetic field
You will be able to: Predict the magnetic field direction produced by a moving charge at a specified observation point.
Which direction is the field beside a moving charge?
A positive charge moves to the right. Consider an observation point above it. The magnetic field there points out of the page. The source velocity and the direction from the source to the observation point together determine this third direction.
A useful starting point: How a material changes the magnetic response →
Words and symbols before equations
- Source charge
- The moving charge producing the field, distinct from a test charge experiencing a force.
- Position vector r
- Arrow from the source’s current position to the observation point.
- Out of page ⊙
- Arrow tip seen head-on; direction toward you.
- Into page ⊗
- Arrow tail seen head-on; direction away from you.
What this picture assumes
Rightward-moving point source, equal source–probe distance. Directions only in a nonrelativistic model; no numerical magnetic-field magnitude is implied.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Positive source moving right, probe above: B out of page.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
For a positive moving source, apply the right-hand rule from velocity toward the source-to-observation direction. The field is perpendicular to both. Reverse the charge sign or reverse velocity and the field direction reverses.
At equal distance and speed, the field is greatest at points perpendicular to the velocity direction and zero along the velocity axis in the nonrelativistic point-charge model. Increasing speed strengthens the field; increasing distance weakens it.
This lesson uses directions and relative trends. The optional model behind these trends has magnitude proportional to |q|v sinθ/r², but no numerical field formula for a moving point charge is needed here. Do not confuse this source-field rule with the force rule q v × B acting on a separate charge.
A worked example, step by step
A positive source moves right. Compare observation points equally far above and below it.
- Choose +x right, +y up and +z out of the page.
- Above the charge: +x crossed toward +y gives +z, out of the page.
- Below the charge: +x toward −y gives −z, into the page.
- Equal distances and perpendicular directions give equal field magnitudes, with opposite directions.
The observation vector points from the source to the observation point, not the other way around.
What if the negative source moves right and the probe is above it?
Compare with an explanation
Reverse the positive-source result: B points into the page.
Predict. Change one thing. Explain.
Keep velocity rightward. Move the observation point above or below, then reverse the source sign. Predict each field direction before using the controls.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Positive source moving right, probe above: B out of page.
Rightward-moving point source, equal source–probe distance. Directions only in a nonrelativistic model; no numerical magnetic-field magnitude is implied.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant field, force, flux 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 negative charge moves right. (a) Draw its velocity. (b) Draw r to a point above. (c) Find the positive-source field direction first. (d) Correct for the negative charge.
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Compare with the answer and four-point rubric
- 1 point: Velocity points right.
- 1 point: r points from charge upward to the probe.
- 1 point: For positive q the field would be out of page.
- 1 point: Negative q reverses it into the page.
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 1Which charge produces this field?
The moving source charge.
RECALL 2What does ⊙ mean?
Out of the page toward the viewer.
RECALL 3Why specify the observation point?
A field assigns a potentially different vector to each location.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
A moving charge produces a magnetic field
- Source-field direction: positive-source v × r̂; reverse for negative q.
- Maximum at perpendicular observation direction; zero on the velocity axis.
- Greater distance weakens the field in the point-source model.
Remember: The observation vector points from the source to the observation point, not the other way around.
Conditions: Rightward-moving point source, equal source–probe distance. Directions only in a nonrelativistic model; no numerical magnetic-field magnitude is implied.
Refresh Kid · AP Physics 2 Unit 4 (official Unit 12) · Objectives 12.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 12.2, objectives 12.2.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the fourth AP Physics 2 unit; College Board numbers it Unit 12; 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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