Electromagnetic Induction Calculator: Magnetic Flux, Faraday's Law, Motional EMF, Inductance and AC Generator
Solve the standard electromagnetic induction problems: flux, Faraday's law, a moving rod, a solenoid and a generator.
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How this calculator works
Choose the problem. For flux enter the field, the area and the angle. For Faraday's law enter the number of turns and how much the field changes in what time.
For a moving rod enter its length and speed. For a solenoid enter its length, turns, area and core, then the current change. For a generator enter the turns, field, area and frequency.
The calculator gives the answer with the steps, and explains Lenz's law, the direction of the induced current.
Formulas used
- \Phi = BA\cos\theta
- \varepsilon = -N\frac{d\Phi}{dt}
- \varepsilon = BLv
- L = \frac{\mu_0\mu_rN^2A}{\ell}
- \varepsilon = NBA\omega\sin\omega t
Worked example
With the default numbers in the calculator above:
- Magnetic flux through one turn: 0.005 Wb (5.00 mWb)
- Flux linkage of the whole coil: 0.5 Wb turns
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? EMF induced by a changing field (Faraday).
- Change in the flux through one turn: 0.004 Wb
- Induced EMF (Faraday's law, size): 2.00 V
- Direction (Lenz's law): The flux is growing, so the induced current makes a field that opposes the increase
Common questions
What does the minus sign mean?
Lenz's law: the induced current is in the direction that opposes the change in flux that causes it.
Why is the EMF largest when the flux is zero in a generator?
The EMF depends on how fast the flux changes, which is fastest when the coil passes through the position of zero flux.
What is a weber?
The unit of magnetic flux. One weber is one tesla through one square metre.
What increases the inductance?
More turns (it goes as the square), a larger area, a shorter coil, and a magnetic core.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any university physics text (Faraday's law, Lenz's law, inductance); Fitzgerald, Kingsley and Umans, Electric Machinery.
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