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Premium experiment • circular field scaling

PHYSICS • MAGNETISM

Magnetic Field Around a Wire

Move a probe around an ideal straight wire and connect current, distance, field strength, and the right-hand rule.

● INTERACTIVEMagnetic Field Around a Wire
Field strength
Probe radius
Field direction
B·r

Reasoning inspector

live model state
Current I—
Probe radius r—
Field B—
Invariant B·r—
Field per amp—
Current direction—
Field circulation—

Explore circular magnetic fields

Change current and distance to see the inverse-radius field law and reverse the current to flip field circulation.

LEARN WITH THE SIMULATION

Understand Magnetic Field Around a Wire by experimenting.

START HERE

A long straight current-carrying wire produces a magnetic field whose direction wraps around the wire and whose ideal magnitude follows B = μ₀I/(2πr). This laboratory turns that proportionality into a scaling experiment: current sets field strength directly, distance weakens it inversely, and reversing current reverses circulation without changing magnitude. The inspector exposes B·r and B/I so learners can test invariants instead of memorizing the formula.

BUILD THE IDEA

What you should understand first

  • Use B = μ₀I/(2πr) to predict field magnitude before reading the probe.
  • Explain why doubling current doubles B while doubling radius halves B.
  • Use the right-hand rule to connect current direction with clockwise or counterclockwise field circulation.
  • Recognize B·r as constant for fixed current and B/I as constant at fixed radius in the ideal infinite-wire model.

TRY IT YOURSELF

Can two different current,radius combinations produce the same magnetic-field magnitude?

  1. Choose a target field and reach it with the default current by changing probe radius.
  2. Double the current and predict the radius required to recover the same target field.
  3. Reverse current direction without changing current magnitude or radius.
  4. Compare magnitude and circulation direction after the reversal.
Read the visual:

Because B depends on the ratio I/r, multiplying both I and r by the same factor leaves the magnitude unchanged. Reversing current changes only the field direction in this model, so the same magnitude appears with opposite circulation.

WHY IT WORKS 01

The 1/r law follows from cylindrical symmetry

For an ideal infinitely long straight wire, every point on a circle of radius r has the same field magnitude and the field is tangent to that circle. Ampère’s law gives B(2πr) = μ₀I, which rearranges to B = μ₀I/(2πr). The simulation’s circular field rings encode that symmetry directly.

WHY IT WORKS 02

Scaling is often more useful than recalculating

If current is fixed, B₁r₁ = B₂r₂, so a field at a new radius can be predicted with a simple ratio. If radius is fixed, B scales directly with I. The inspector’s B·r and B/I quantities let learners test these two proportionalities numerically across many settings without repeatedly substituting constants.

WHY IT WORKS 03

Direction contains information that magnitude alone loses

The field magnitude formula uses the magnitude of current, but the vector direction comes from the right-hand rule. Current out of the page produces one circulation sense and current into the page produces the opposite. A sensor measuring only magnitude could not distinguish those two current directions without directional information.

DO NOT MIX THESE UP

Common misconception

Magnetic field lines around a straight wire are circular, not radial arrows pointing away from the conductor. Reversing current reverses field direction but not magnitude at the same |I| and r. The 1/r law is for an ideal effectively infinite straight wire; finite wires, nearby conductors and magnetic materials can alter the field.

PRACTICE CHALLENGE

Can you reach a target magnetic field using two different current,radius pairs and explain why both solutions work?

  • Set a target field and tune current or radius until it is reached.
  • Record I/r and the B·r inspector value.
  • Choose a different current and predict the radius that preserves I/r.
  • Verify the target again, then reverse current direction and explain what changes and what does not.
Reveal the reasoning

The ideal field magnitude depends only on I/r, so any two settings with the same ratio produce the same B. For fixed I, B·r is constant; for fixed r, B/I is constant. Reversing current changes the field’s circulation direction while leaving its magnitude unchanged if |I| and r are unchanged.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • The conductor is modeled as an infinitely long straight wire carrying steady current.
  • The surrounding medium is treated as vacuum with permeability μ₀.
  • The probe distance is measured perpendicular to the wire axis and the current is constant.

Model limitations

  • Finite wire length, nearby conductors, magnetic materials, and time-varying currents can change the real field.
  • The model does not include electric fields, induction effects, conductor thickness, or relativistic corrections.

CONNECT IT

Where this matters

  • Current sensing and Hall-effect measurements
  • Power cables, busbars and magnetic-clearance estimates
  • Laboratory verification of the right-hand rule
  • Building intuition for Ampère’s law

WORDS THAT MATTER

Key vocabulary

Magnetic field
Vector field describing magnetic influence, measured in tesla.
Permeability of free space
Constant μ₀ connecting current and magnetic field in the ideal vacuum-wire relation.
Right-hand rule
Direction convention linking current direction to circular magnetic-field circulation.
Ampère’s law
Relation between magnetic-field circulation and enclosed electric current.
Inverse-distance scaling
Dependence proportional to 1/r, so doubling distance halves the ideal field.