• Black Magnetic Dipole physics hoodie, pixel-art magnetic dipole field design, worn by a model, front close-up
  • Black Magnetic Dipole physics hoodie, pixel-art magnetic dipole field design, worn by a model, back close-up
  • Black Magnetic Dipole physics hoodie, pixel-art magnetic dipole field design, front view
  • Black Magnetic Dipole physics hoodie, pixel-art magnetic dipole field design, back view
  • Black Magnetic Dipole physics hoodie, pixel-art magnetic dipole field design, turning on a model
  • Black Magnetic Dipole physics hoodie, ΨP Pixelated Physics neck label
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Magnetic Dipole HoodieEVERY LINE COMES HOME | Pixelated Physics

Magnetic Dipole Hoodie – EVERY LINE COMES HOME | Pixelated Physics

$54.99 USD
$54.99 USD
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Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Color
Black
Size
S–5XL
Made
To order · shipping times

Electric field lines start and stop on charges. Magnetic field lines have nowhere to start. The exact field lines of a magnetic dipole, r = C sin²θ, around a pixel bar magnet. ∇·B = 0, so every line closes on itself. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

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

Electric field lines start and stop on charges. Magnetic field lines have nowhere to start.

That is what ∇·B = 0 says, one of Maxwell’s equations. For a dipole the lines solve exactly to r = C sin²θ: each leaves the north end, swings out and returns to the south end, then continues through the magnet to close the loop.

In the art the brightness steps with field strength, which falls as 1/r³. The small bar magnet covers the centre, where the ideal point-dipole field is singular.

A magnetic monopole would break the rule. Many experiments have searched for one, and none has been found.

Every line comes home.

Equations

\[\nabla\cdot\mathbf{B} = 0\]
\[\mathbf{B} = \frac{\mu_0}{4\pi}\,\frac{3(\mathbf{m}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}} - \mathbf{m}}{r^3}\]
\[r = C\sin^2\theta\;\text{(field lines)}\]
SymbolMeaningUnit
\(\mathbf{B}\) magnetic field \(\mathrm{T}\)
\(\mu_0\) vacuum permeability \(\mathrm{N/A^2}\)
\(\mathbf{m}\) magnetic dipole moment \(\mathrm{A·m^2}\)
\(\hat{\mathbf{r}}\) unit vector from the dipole \(\mathrm{1}\)
\(r\) distance from the dipole \(\mathrm{m}\)
\(\theta\) angle from the dipole axis \(\mathrm{rad}\)
\(C\) constant labelling one field line \(\mathrm{m}\)

Sources

  1. Maxwell (1865) A Dynamical Theory of the Electromagnetic Field, Phil. Trans. R. Soc. 155, 459
  2. Jackson, Classical Electrodynamics, 3rd ed. (1999), Sec. 5.6
  3. Griffiths, Introduction to Electrodynamics, Ch. 5
  4. Particle Data Group, Review of Particle Physics: Magnetic monopole searches
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Field notes

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