Magnetic Flux Calculator
What threads the loop: Φ = B·A·cosθ with the tilt card live, and Faraday's pull-out bill — the EMF a collapsing flux owes every circuit it leaves.
Magnetic Flux Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Uniform field over the loop assumed
- Single turn; multiply EMF by N yourself
In short: A fridge-magnet field (≈ 5 mT) face-on through 100 cm² of loop: Φ = B·A = 50.000000 µWb. The tilt card keeps the books: turn the loop edge-on (90°) and the flux reads 0.000000 — cosθ is exact, quantized so edge-on fires cleanly. The Faraday card is the one that runs the world: yank the loop fully out in 0.1 s and the collapsing flux induces E = Φ/t = 0.500000 mV — every generator, every induction hob, every card reader is this card at scale. Change the flux, owe the voltage.
Formula
Φ = B·A·cosθ · EMF = −N·ΔΦ/Δt · edge-on: cos 90° = 0
Flux is how much field threads a loop: field strength times face-on area, with cosθ discounting the tilt. It is the field's ACCOUNTING, not a new force — and its law of change is Faraday's: a collapsing flux induces a voltage proportional to how fast it collapses. Every generator on Earth is this card being deliberately, continuously imposed.
Worked Example
- Enter the field, the loop's area and the tilt.
- Read Φ in webers (micro-webers are the honest unit at tabletop scale).
- Use the tilt card to see cosθ keep the books.
- Price the pull-out: the induced EMF your change of flux owes.
Defaults: 50.000000 µWb; edge-on 0.000000; pull-out in 0.1 s induces 0.500000 mV.
Strengths & Limits Of This Model
Where this engine is strong
- Edge-on branch quantized to a clean zero
- Faraday card prices the pull-out honestly
Where it stops
- No Lenz-current feedback
- No non-uniform field integration
Practical Use Cases
Generators
the EMF behind the spin
Induction design
hobs, chargers, pickups
Teaching
Faraday's law with a bill attached
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Magnetic Flux Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does the tilt discount by cosθ?
Because only the field component SQUARE to the loop threads it: tilt the loop and the effective field is B·cosθ, dying to zero exactly edge-on. The page quantizes cos at machine precision so the 90° case reads a clean 0.000000, not 3e-17.
What is a weber?
One weber is one tesla through one square metre — field times area, the flux account. Tabletop numbers live in micro-webers, which is why the hero prints both. Change webers per second and you have volts: the units of Faraday's law chain that directly.
Why does CHANGING flux induce voltage?
Faraday's law: a loop cares about the flux through it, and nature charges for changes — EMF = −N·ΔΦ/Δt, the minus sign pointing against the change (Lenz's law). Hold the flux steady and the loop is content; collapse it and the loop pushes current to protest.
Is a generator just this card?
Yes, spun: a coil rotating in a field sweeps cosθ from +1 to −1 and back, so the flux swings and the induced voltage alternates — mains electricity is Faraday's card at 50 or 60 hertz. The page's pull-out is one stroke of that wheel.
Why is zero field an answer, not an error?
A loop in a field-free zone threads nothing, honestly: Φ = 0. It differs from the tilt's zero — there the field is real but edge-on; here it is simply absent. Both are honest zeros; the cards say which is which.
Does the loop's material matter?
For the FLUX, no — geometry only. The material matters for what the induced EMF drives: a copper ring carries big currents (induction hobs), a plastic hoop carries none but the voltage is there, measurable, all the same.
How does N turns change things?
N turns thread N times the flux, so the induced EMF multiplies by N — generators wind thousands of turns for exactly this reason. The page prices one loop; multiply honestly for your winding.
How does this pair with the field page?
As product and source: that page computes the B your coil makes; this page multiplies it through a loop and prices what happens when it changes. Drive this page's field chip from the solenoid's number and the two pages chain into one experiment.