Why are there no field-line curves in ring mode?

In the plane of a flat loop, the modeled B field from the loop currents is perpendicular to that plane (only a z-component in this 2D slice), so there is no in-plane vector field to trace as streamlines; the heatmap shows |B_z| instead.

How does this relate to the Magnetic Field visualizer?

That page uses idealized dipole and wire models for interaction. Here the wire and loop are fixed geometries tied to textbook Biot–Savart formulas and discrete segmentation.

Biot–Savart Law

Infinite wire B ∝ 1/r; ring via segment sum; heatmap + probe.

About this model

The infinite straight wire uses the analytic azimuthal field B ∝ 1/r in the plane perpendicular to the current, with circular streamlines integrated along B. The circular loop sums many short current-element contributions to the z-component of B in the plane of the loop using the Biot–Savart cross-product rule; simulation constants absorb μ₀/(2π) and μ₀/(4π) into unity for relative plots.

Who it's for: Introductory magnetostatics after the generic magnetic-field sandbox; emphasizes explicit Biot–Savart summation for a loop.

Key terms

Biot–Savart law
magnetic field
steady current
straight wire
current loop

How it works

The Biot–Savart law builds B from steady currents: an infinite straight wire has circular field lines in the perpendicular plane with magnitude B ∝ 1/r; a flat circular loop is modeled by summing many short current elements so you see how B_z varies in the plane of the loop (including the sign flip across the ring).

Key equations

dB = (μ₀/4π) I dl × r̂ / r²

Long wire: B = μ₀ I / (2π r) (tangential)

Sim units: μ₀/(2π) and μ₀/(4π) set to 1

Frequently asked questions

Why are there no field-line curves in ring mode?: In the plane of a flat loop, the modeled B field from the loop currents is perpendicular to that plane (only a z-component in this 2D slice), so there is no in-plane vector field to trace as streamlines; the heatmap shows |B_z| instead.
How does this relate to the Magnetic Field visualizer?: That page uses idealized dipole and wire models for interaction. Here the wire and loop are fixed geometries tied to textbook Biot–Savart formulas and discrete segmentation.

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