Read induced polarity from changes in a flux record

Establish the model and evidence

Faraday’s law relates average induced emf to flux change: emf=−NΔΦ/Δt for N turns with the same per-turn flux. The minus sign encodes Lenz’s law: induced current, if a closed path permits it, produces a field that opposes the change in flux. It does not always oppose the original field; when the original field is decreasing, the response can support it.

The original record ramps a +z field upward, holds it constant, then ramps it down. Area and normal remain fixed. The flux-time slope is positive, zero and negative in the three intervals, so the induced emf is negative, zero and positive under the stated circulation convention. The plateau has the largest flux but no induced emf. This is a direct test of slope reasoning rather than reading graph height.

The chosen +z normal defines counterclockwise circulation as positive when viewed from +z. Increasing +z flux induces clockwise current, whose field is −z. Decreasing +z flux induces counterclockwise current, whose field supports +z. Flipping the chosen normal reverses the signed labels but must leave the physical clockwise/counterclockwise prediction unchanged.

The ideal piecewise-linear record has abrupt slope changes, so interval values exclude the corner instants rather than assigning an arbitrary derivative there. The model also assumes negligible self-inductance and a closed 10 Ω resistive circuit. An open circuit can have induced emf without sustained current. The external agent changing the field supplies the energy that becomes resistor heat; this record is not a self-powered generator.

Worked evidence

For 20 turns, area 0.010 m² and B rising from 0.10 to 0.40 T in 0.20 s, per-turn flux changes by 0.0030 Wb. The ramp emf is −0.30 V and current −0.030 A. The hold emf is zero; the equal-duration return ramp gives +0.30 V.

Predict and investigate

Will the induced emf be largest during the plateau where flux is largest?

Capture 20 turns and ramp duration 0.20 s. Reconstruct all three interval polarities and currents. Double the turns, then separately double duration, explaining the emf and total resistor-heat changes using the declared 10 Ω assumption.

Transfer to changed conditions

A 30-turn coil’s per-turn flux falls from 4 mWb to 1 mWb in 0.15 s. Find average signed emf with the original normal held fixed, and current if total resistance is 12 Ω.

Compare the worked transfer

ΔΦ=−0.003 Wb, so emf=+0.60 V and signed current=+0.050 A. The physical circulation follows the positive orientation associated with the chosen normal. The result is an interval average, not a claim about an unspecified detailed waveform.

Explain the boundary

Explain why Lenz’s law opposes a change rather than always opposing the existing field, and name the energy source.

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.