Infer field direction and cancellation from two currents

Establish the model and evidence

A long straight current produces a magnetic field that circles the wire rather than pointing along it. For a thin wire in vacuum, B=μ₀|I|/(2πr), where r is perpendicular distance from the wire axis. The approximation neglects finite ends and the internal field inside a real wire. The direction follows curled fingers around the conventional current direction, not electron drift.

The left wire sits at x=−0.05 m and carries +3 A out of the page. At a point to its right, its field is +y. The right wire sits at x=+0.05 m; a positive current there gives −y field at points to its left. Signed y components can therefore cancel between same-direction currents, while opposite-direction currents reinforce there.

Only at equal distances and equal current magnitudes is the midpoint cancellation guaranteed. Changing one current or moving the observation point changes the relative magnitudes. Add vector components rather than subtracting magnitudes by habit. A zero net field at one point does not imply that either source switched off or that the surrounding field is zero.

A current loop produces a field through its center along the loop axis; curl fingers with conventional circulation and the thumb indicates the axial direction. This connects current-generated fields with dipole-like behavior. Magnetic permeability can differ in surrounding materials, so the vacuum formula should not be applied unchanged near a magnetic core. The experiment is a computed field map, not a real current or compass measurement.

Worked evidence

At the midpoint, each +3 A wire is 0.05 m away and contributes 12 µT in opposite y directions, giving zero. Reversing the right current to −3 A makes both contributions +12 µT, giving +24 µT. Moving away from the midpoint destroys the equal-distance symmetry.

Predict and investigate

If the right current reverses, will the field cancel or reinforce between the wires?

Compare right currents +3 and −3 A at x=0, then repeat at x=+0.02 m. Reconstruct each signed contribution using its actual distance and explain the changed cancellation.

Transfer to changed conditions

A single long wire carries 4 A. Using μ₀/(2π)=2×10⁻⁷ T m/A, find field magnitude at 0.020 m and at 0.040 m. Describe the effect of reversing current.

Compare the worked transfer

The fields are 40 µT and 20 µT. Reversing current reverses the circular field direction without changing either magnitude. The inverse-distance law is not the inverse-square point-charge field law.

Explain the boundary

What independent background-field or position check would be necessary before inferring a current from a real compass deflection?

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original prose, computed diagrams and synthetic/model evidence, not completed laboratory measurements. All activities are virtual. No strong-magnet handling, high-current wiring, beam equipment or moving-conductor apparatus is requested; authentic practical work requires qualified supervision and a separately approved safety procedure.