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Plasma Drift

E × B Drift Physics

\[\mathbf{v}_E = \frac{\mathbf{E}\times\mathbf{B}}{B^{2}}\]
$21.99 USD
$21.99 USD
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Meet Plasma Drift. Heat a gas until its atoms come apart and it becomes plasma. In crossed electric and magnetic fields, electrons and ions circle opposite ways, yet both drift the same direction at the same speed. On the mug: v_E = E × B / B². Pixel-art full-wrap 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

In crossed electric and magnetic fields, charged particles drift at v_E = E×B/B² regardless of charge or mass. E = 1000 V/m and B = 0.1 T give 10 km/s.

Plasma Drift moves where the fields tell it, and so do all its electrons and ions.

Heat a gas until its atoms lose electrons and it becomes a plasma, a soup of free charges. Irving Langmuir gave it that name in 1928. Plasma fills the Sun, lightning and fusion machines.

Put a plasma in crossed electric and magnetic fields. Each charge circles around the magnetic field, ions one way and electrons the other. The electric field speeds a particle up on one side of its circle and slows it on the other, so the loop does not close and the particle drifts sideways. The drift velocity is v_E = E × B/B², the formula on this mug. It contains no charge and no mass, so electrons and ions drift in the same direction at the same speed, and no current flows.

A worked number: E = 1000 V/m across B = 0.1 T gives v_E = E/B = 10 km/s, for every particle alike.

“Opposite spins, same road,” says Plasma Drift. “Everyone goes my way.”

Equations

\[\mathbf{v}_E = \frac{\mathbf{E}\times\mathbf{B}}{B^{2}}\]
\[|\mathbf{v}_E| = \frac{E}{B}\quad(\mathbf{E}\perp\mathbf{B})\]
SymbolMeaningUnit
\(\mathbf{v}_E\) E×B drift velocity of the guiding centre \(\mathrm{m/s}\)
\(\mathbf{E}\) electric field \(\mathrm{V/m}\)
\(\mathbf{B}\) magnetic flux density \(\mathrm{T}\)
\(B\) magnitude of B \(\mathrm{T}\)
\(E\) magnitude of E \(\mathrm{V/m}\)

Sources

  1. Chen (2016) Introduction to Plasma Physics and Controlled Fusion, 3rd ed., Springer, §2.2
  2. Langmuir (1928) Oscillations in Ionized Gases, PNAS 14, 627

Source Langmuir, I. (1928). Oscillations in Ionized Gases. Proceedings of the National Academy of Sciences 14, 627–637.doi.org/10.1073/pnas.14.8.627

Field notes

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