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Faradax

Faraday’s Law Physics

\[\mathcal{E} = -\frac{d\Phi_B}{dt}\]
$21.99 USD
$21.99 USD
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How does a generator make electricity? Faradax answers change with change. Faraday’s law says a changing magnetic flux through a loop induces a voltage, E = −dΦB/dt. The minus sign is Lenz’s law: the induced current opposes the change. Generators, transformers and induction hobs all rely on it. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A changing magnetic flux through a loop induces a voltage around it. The minus sign means the induced current opposes the change that caused it, which is Lenz's law.

Faradax answers change with change.

In 1831 Michael Faraday found that a changing magnetic field drives a current in a nearby loop of wire, and published his experiments the next year. It does not matter how the change happens: move a magnet, move the coil, or turn a current on and off. The induced voltage equals how fast the magnetic flux through the loop changes, the equation on this mug.

The minus sign is Lenz's law, from Heinrich Lenz in 1834. The induced current always flows so that its own magnetic field opposes the change that caused it. CHANGE ME. I PUSH BACK. That is why a magnet falling through a copper pipe slows down, and why it takes effort to turn a generator that is supplying current.

Generators, transformers, induction hobs, electric guitar pickups and wireless chargers all run on it. It is also one of Maxwell's four equations.

Faradax does nothing while things stay still. Change something, and he answers.

Equations

\[\mathcal{E} = -\frac{d\Phi_B}{dt}\]
\[\Phi_B = \int \vec B\cdot d\vec A\]
SymbolMeaningUnit
\(\mathcal{E}\) electromotive force (induced voltage) around the loop \(\mathrm{V}\)
\(\Phi_B\) magnetic flux through the loop \(\mathrm{Wb}\)
\(t\) time \(\mathrm{s}\)
\(\vec B\) magnetic flux density \(\mathrm{T}\)
\(d\vec A\) small element of area spanning the loop, normal to the surface \(\mathrm{m²}\)

Sources

  1. Faraday (1832) Experimental Researches in Electricity, Phil. Trans. R. Soc. 122, 125
  2. Lenz (1834) Ueber die Bestimmung der Richtung der durch elektrodynamische Vertheilung erregten galvanischen Ströme, Ann. Phys. 107, 483
  3. HyperPhysics — Faraday's Law
  4. Feynman Lectures on Physics Vol. II Ch. 17: The Laws of Induction

Source Faraday, M. (1832). Experimental researches in electricity. Philosophical Transactions of the Royal Society of London, 125–162.doi.org/10.1098/rstl.1832.0006

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