• Black Field Lines physics hoodie, pixel-art electric quadrupole field design, worn by a model, front close-up
  • Black Field Lines physics hoodie, pixel-art electric quadrupole field design, worn by a model, back close-up
  • Black Field Lines physics hoodie, pixel-art electric quadrupole field design, front view
  • Black Field Lines physics hoodie, pixel-art electric quadrupole field design, back view
  • Black Field Lines physics hoodie, pixel-art electric quadrupole field design, turning on a model
  • Black Field Lines physics hoodie, ΨP Pixelated Physics neck label
1 6

Field Lines HoodieSTART POSITIVE | Pixelated Physics

Field Lines Hoodie – START POSITIVE | Pixelated Physics

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

Four charges sit on the corners of a square: plus, minus, plus, minus. Total charge zero. Total dipole moment zero too. What is left is a quadrupole. The exact field of an electric quadrupole, +q −q +q −q. Every line leaves a positive charge, ends on a negative one. Net charge zero. 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

Four charges sit on the corners of a square: plus, minus, plus, minus. Total charge zero. Total dipole moment zero too. What is left is a quadrupole.

Every line in the art was traced through the exact field, the plain sum of four Coulomb terms on the back, stepped along E with a Runge–Kutta integrator. Fourteen lines leave each positive charge at equal angles.

Gauss’s law, ∇·E = ρ/ε₀, does the bookkeeping. Field lines begin only on positive charge and end only on negative charge. With the books balanced, no line here needs to go to infinity, though a few leave the frame before they close.

The faint cross is the equipotential V = 0. By symmetry it is exactly the two axes: every point on them is equally far from a plus and a minus of the same size.

From far away, a quadrupole’s field falls off as 1/r⁴, two powers faster than a single charge. Up close, every line starts positive.

Equations

\[\nabla\cdot\mathbf{E} = \frac{\rho}{\varepsilon_0}\]
\[\mathbf{E}(\mathbf{r}) = \sum_i \frac{k\,q_i\,(\mathbf{r}-\mathbf{r}_i)}{|\mathbf{r}-\mathbf{r}_i|^3},\qquad k = \frac{1}{4\pi\varepsilon_0}\]
SymbolMeaningUnit
\(\mathbf{E}\) electric field \(\mathrm{V/m}\)
\(\rho\) electric charge density \(\mathrm{C/m^3}\)
\(\varepsilon_0\) vacuum permittivity \(\mathrm{F/m}\)
\(k\) Coulomb constant, 1/(4\pi\varepsilon_0) \(\mathrm{N·m^2·C^{-2}}\)
\(q_i\) charge of the i-th point charge (here +q, −q, +q, −q) \(\mathrm{C}\)
\(\mathbf{r}\) point where the field is evaluated \(\mathrm{m}\)
\(\mathbf{r}_i\) position of the i-th charge \(\mathrm{m}\)

Sources

  1. Coulomb (1785) Premier mémoire sur l’électricité et le magnétisme, Histoire de l’Académie Royale des Sciences
  2. Jackson, Classical Electrodynamics, 3rd ed. (1999), Ch. 1 and Ch. 4: Multipoles
  3. Griffiths, Introduction to Electrodynamics, Ch. 2: Electrostatics
  4. Feynman Lectures on Physics Vol. II Ch. 4: Electrostatics
View full details

Field notes

View all
1 3
View all