Magnetism and Current-Carrying Wires
Electric current produces a magnetic field, and an external magnetic field can exert a force on a current-carrying wire. Around a long straight wire, the field circles the wire and decreases as 1/r; fields from multiple wires combine by vector addition.
Magnetism and Current-Carrying Wires: quick answer
Electric current produces a magnetic field, and an external magnetic field can exert a force on a current-carrying wire. Around a long straight wire, the field circles the wire and decreases as 1/r; fields from multiple wires combine by vector addition. Current is moving charge in bulk, so it both creates magnetic fields and experiences magnetic force. Topic 12.3 connects field-source reasoning, inverse-distance behavior, vector superposition, and force on a wire without using the calculus machinery reserved for a more advanced course.
Use the algebra-based long-straight-wire result and vector superposition. Do not introduce Biot–Savart integrals, Ampère-law line integrals, or calculus-based field derivations. Use conventional-current direction in current-based right-hand rules.
What you should be able to explain and do
Use these as closed-note retrieval prompts before opening the worked examples.
Use the right-hand rule to determine the circular field direction around a straight current-carrying wire.
Use B=μ₀I/(2πr) and predict factor changes with current and distance.
Use vector superposition for magnetic fields from multiple wires.
Determine the magnitude and direction of magnetic force on a current-carrying wire.
Key terms you need for this lesson
Keep the vocabulary next to the model so direction and representation reasoning never depend on an unexplained term.
current-carrying wire
current-carrying wire is a conductor with net charge flow that produces a magnetic field.
perpendicular distance
perpendicular distance is the shortest distance from the wire’s central axis to the field point.
field superposition
field superposition is vector addition of magnetic fields from multiple sources.
wire-force direction
wire-force direction is the direction given by the right-hand relationship among conventional current, external B, and force.
length in field
length in field is the portion ℓ of a straight wire segment actually immersed in the magnetic-field region.
conventional current
conventional current is the positive-charge reference direction used in current-based magnetic right-hand rules.
Match every expression to its source, geometry, and scope
The relationship, variable meanings, conditions, and physical anchor stay together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
B = μ₀I/(2πr) | B magnetic field (T); μ₀ vacuum permeability (T·m/A); I current (A); r perpendicular distance from wire axis (m) | long straight current-carrying wire in free space | doubling I doubles B; doubling r halves B |
F_B = IℓB sinθ | F_B magnetic-force magnitude (N); I current (A); ℓ wire length inside the field (m); B external field (T); θ angle between current direction and B | straight current segment in a magnetic field | a wire perpendicular to B experiences maximum force; a parallel wire experiences zero force |
B_net = vector sum of source fields | B_net and source fields measured in tesla; directions determined before adding | two or more current-carrying wires contribute magnetic field at one location | fields in opposite directions subtract in magnitude, while fields in the same direction add |
What a strong magnetic diagram or graph must show
Use geometry and direction first, then connect the diagram or graph to the mathematical relationship.
Long-wire field map
concentric circles centered on the wire with tangent B vectors.
B-versus-r graph
inverse relationship for a fixed current in the long-straight-wire model.
Two-wire field map
determine each source-field direction first, then add vectors at the point of interest.
I–B–F wire diagram
current direction and external field determine the force direction on the wire segment.
Change one magnetic condition and inspect what responds
Make a prediction first. Then move one control and explain the result using the governing geometry, proportionality, and direction rule.
Two examples with the model choice exposed
The solution shows why the relationship applies rather than only substituting numbers.
Field from a straight wire
Situation: A long wire carries 4.0 A. Find B at r=0.020 m.
Reasoning: Use B=μ₀I/(2πr) because the source is a long straight wire and r is perpendicular distance.
B=(4π×10⁻⁷)(4.0)/(2π×0.020)=4.0×10⁻⁵ T.
Force factor change
Situation: A straight wire segment is perpendicular to a uniform magnetic field. The current doubles while ℓ and B stay fixed.
Reasoning: For θ=90°, F_B=IℓB, so force is directly proportional to current.
The magnetic-force magnitude doubles; direction is unchanged if current direction is unchanged.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 12.3?
Use current-carrying-wire magnetism when currents create fields or when a wire carrying conventional current sits in an external magnetic field.
How this idea fits the course
This connects circuit current from Unit 11 to magnetic fields and prepares the changing-flux induction ideas of 12.4.
Scope check before solving
Use the algebra-based long-straight-wire result and vector superposition. Do not introduce Biot–Savart integrals, Ampère-law line integrals, or calculus-based field derivations. Use conventional-current direction in current-based right-hand rules.
Turn the topic into measurable magnetic evidence
Control geometry and orientation explicitly; magnetism experiments fail quickly when direction or distance is not defined.
Investigation target
Measure magnetic-field strength versus current and distance from a long straight wire, or measure force on a current-carrying wire versus current, and test the predicted proportionality.
Reasoning errors to eliminate
Repair the field/force/flux model before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can distinguish the magnetic-field source from the object experiencing magnetic force.
- I can determine magnetic direction before substituting into a magnitude equation.
- I can define every quantity I use and state its SI unit where applicable.
- I can translate among field maps, right-hand-rule diagrams, graphs, and equations.
- I can state the topic boundary and avoid calculus-based magnetism that is outside this unit.
- I can design or critique a magnetic experiment and justify a claim from measured evidence.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 12.3 FAQs
What shape is the field around a long straight wire?
The field is tangent to concentric circles centered on the wire.
How does B depend on current?
For fixed distance in the long-wire model, B is directly proportional to current.
How does B depend on distance?
For fixed current, B is inversely proportional to perpendicular distance r.
How do several wires affect one point?
Find each wire’s magnetic-field vector at that point and add the vectors.
What length goes into F=IℓB sinθ?
Use the length of the wire segment that lies within the magnetic-field region.
Which current direction should I use for the right-hand rule?
Use conventional current unless the problem explicitly asks about electron motion.