Flux depends on field through an area
You will be able to: Calculate signed magnetic flux using a surface normal and distinguish flux from field strength.
Which angle belongs in magnetic flux?
A flat loop can face a field directly or turn edge-on. The field strength can stay unchanged while the amount of field through the loop’s area changes. A perpendicular arrow called the surface normal makes the angle unambiguous.
A useful starting point: One wire’s field acts on the other wire →
Words and symbols before equations
- Magnetic flux Φ_B
- Signed measure of B through a chosen surface; unit weber (Wb)=T·m².
- Area A
- Surface area enclosed by a loop, in m².
- Surface normal
- An arrow perpendicular to the surface; choose one of its two directions and keep that convention.
- Angle θ
- Angle between B and the chosen normal, not between B and the plane.
What this picture assumes
Uniform B=0.50 T upward over a flat loop. Chosen normal is rotated in the xy plane. Φ=BA cosθ. Spatial projection and edge view are orientation guides; displayed area value sets physical size.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Φ_B=BA cosθ=0.01 Wb. Positive component along chosen normal.
- 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 uniform B over a flat surface, Φ_B=BA cosθ. When B is parallel to the normal, θ=0° and flux is +BA. When B lies in the plane, θ=90° and flux is zero.
Reversing the chosen normal reverses the sign of flux without changing the physical field. With one fixed normal, reversing B also reverses flux. A negative flux is an orientation statement, not a negative field magnitude.
The spatial diagram shows a loop, its normal and B; the side view explains the same angle on a flat diagram. Flux can change because field, area or orientation changes. A field being present is not enough to guarantee induction: its flux must change.
| Quantity | Magnetic field B | Magnetic flux Φ |
|---|---|---|
| Description | Vector at a point | Signed field through a surface |
| Unit | Tesla (T) | Weber (Wb) |
| Depends on chosen area? | No | Yes |
A worked example, step by step
A loop of area 0.020 m² is in uniform B=0.50 T with B parallel to its chosen normal. Find flux, then turn it edge-on.
- Initial θ=0°, so cosθ=1.
- Φ_B=(0.50)(0.020)=0.010 Wb.
- Edge-on means B lies in the surface: θ=90° to its normal.
- Flux becomes zero even though B remains 0.50 T.
The cosine angle is measured to the normal. Using the angle to the plane exchanges sine and cosine.
Can the flux be zero while B is nonzero?
Compare with an explanation
Yes. If B lies in the loop’s plane, its perpendicular component is zero.
Predict. Change one thing. Explain.
Rotate the loop normal from 0° through 90° to 180° relative to B. Predict the sign and magnitude using the normal, then compare both views.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Φ_B=BA cosθ=0.01 Wb. Positive component along chosen normal.
Uniform B=0.50 T upward over a flat loop. Chosen normal is rotated in the xy plane. Φ=BA cosθ. Spatial projection and edge view are orientation guides; displayed area value sets physical size.
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 questionB=0.20 T and A=0.030 m². Find flux for (a) θ=0°, (b) θ=90°, (c) θ=180°, and (d) name two physical ways to change flux besides turning the loop.
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Compare with the answer and four-point rubric
- 1 point: +0.0060 Wb.
- 1 point: 0 Wb.
- 1 point: −0.0060 Wb.
- 1 point: Change B or change the enclosed area, with other quantities fixed.
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 is the flux unit?
Weber, Wb.
RECALL 2What is a normal?
A direction perpendicular to the surface.
RECALL 3Does larger B always mean changing flux?
No. A large constant field through a fixed surface can give constant flux.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Flux depends on field through an area
- Uniform field, flat surface: Φ_B=BA cosθ.
- θ is between B and the chosen surface normal.
- 1 Wb=1 T·m².
Remember: The cosine angle is measured to the normal. Using the angle to the plane exchanges sine and cosine.
Conditions: Uniform B=0.50 T upward over a flat loop. Chosen normal is rotated in the xy plane. Φ=BA cosθ. Spatial projection and edge view are orientation guides; displayed area value sets physical size.
Refresh Kid · AP Physics 2 Unit 4 (official Unit 12) · Objectives 12.4.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 12.4, objectives 12.4.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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