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Magnetic Dipole Hoodie

EVERY LINE COMES HOME | Pixelated Physics

\[\nabla\cdot\mathbf{B} = 0\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

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.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

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.

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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

Magnetic field lines never start or stop, because there are no magnetic charges. A dipole's lines leave its north end and loop back to its south, along the curves r = C sin²θ.

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

Source Maxwell, J. C. (1865). A dynamical theory of the electromagnetic field. Philosophical Transactions of the Royal Society of London, 459–512.doi.org/10.1098/rstl.1865.0008

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Field notes

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