Add fields at the same observation point
You will be able to: Determine a loop’s axial field direction and combine signed fields from two wires.
When do magnetic fields reinforce or cancel?
Two current-carrying wires each contribute a field at the midpoint between them. Find those directions separately before adding. Equal currents can cancel or reinforce there depending on their directions.
A useful starting point: Current makes a field around a wire →
Words and symbols before equations
- Superposition
- The net field at one point is the vector sum of all source contributions.
- Loop axis
- Line perpendicular to the plane of a current loop through its center.
- Signed field component
- A field contribution expressed as positive or negative along a chosen axis.
What this picture assumes
Wires at x=−0.10 m and +0.10 m; midpoint probe x=0. Left current is 5 A outward. Vacuum, long straight wires. Positive field component is upward. Loop inset is a separate direction reminder, not a third source.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- At midpoint: B_left=+10 μT; B_right=-10 μT; B_net=0 μT (cancels).
- 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 circular current loop, curl right-hand fingers with conventional current; the thumb gives the field direction along its central axis. Counterclockwise current viewed from the front produces an outward field at the center.
For two parallel long wires with equal outward currents, the midpoint field from the left wire points up and that from the right wire points down. Equal magnitudes cancel. Reverse the right current and both midpoint fields point up, so they add.
Zero net field at one point does not mean each source field vanishes or that the field is zero everywhere. For non-collinear contributions, add components as in other vector problems; never add magnitudes without checking direction.
A worked example, step by step
Two wires 0.20 m apart carry 5 A each out of the page. Find net B at their midpoint, then reverse the right current.
- The midpoint is 0.10 m from each wire.
- Each field magnitude is 10 μT using the long-wire relation.
- With both currents outward, contributions are +10 μT up and −10 μT down: net zero.
- With the right current inward, both point up: net B=20 μT upward.
Add source fields evaluated at the same point, not fields at different positions.
Does net B=0 at the midpoint imply no current in either wire?
Compare with an explanation
No. Nonzero source fields can cancel at that point.
Predict. Change one thing. Explain.
Reverse the right-wire current and vary its magnitude. Compare each midpoint contribution and the signed sum; the loop inset reminds you of the separate axial-field rule.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
At midpoint: B_left=+10 μT; B_right=-10 μT; B_net=0 μT (cancels).
Wires at x=−0.10 m and +0.10 m; midpoint probe x=0. Left current is 5 A outward. Vacuum, long straight wires. Positive field component is upward. Loop inset is a separate direction reminder, not a third source.
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 questionAt one point, wire A produces 8 μT upward and wire B produces 5 μT downward. (a) Choose a positive axis. (b) Find net B. (c) Reverse B’s current and find the new net. (d) Explain why magnitude-only addition failed originally.
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Compare with the answer and four-point rubric
- 1 point: Choose upward positive.
- 1 point: 8−5=3 μT upward.
- 1 point: 8+5=13 μT upward.
- 1 point: Original vectors had opposite directions, so their signed components subtract.
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 1How do multiple magnetic fields combine?
By vector addition at a common observation point.
RECALL 2What sets a loop’s axial field direction?
The conventional current circulation and right-hand rule.
RECALL 3Can cancellation be limited to one location?
Yes; source distances and directions change elsewhere.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Add fields at the same observation point
- B_net=ΣB_source as vectors.
- Loop: fingers along conventional current, thumb gives axial B.
- Cancellation at one point is a local result.
Remember: Add source fields evaluated at the same point, not fields at different positions.
Conditions: Wires at x=−0.10 m and +0.10 m; midpoint probe x=0. Left current is 5 A outward. Vacuum, long straight wires. Positive field component is upward. Loop inset is a separate direction reminder, not a third source.
Refresh Kid · AP Physics 2 Unit 4 (official Unit 12) · Objectives 12.3.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 12.3, objectives 12.3.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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