Why are the field lines around a wire circles, but they curve between the poles of a magnet?

The geometry of the source dictates the field shape. A long, straight wire has a symmetrical cylindrical geometry, so the field lines form concentric circles around it. A bar magnet is a dipole, with a north and south pole; outside the magnet, field lines leave the north pole and enter the south pole, creating the characteristic curved arcs. Both patterns are solutions to the fundamental magnetic field equations for their respective source geometries.

Can magnetic field lines ever cross?

No. At any point in space, the magnetic field has a single, unique direction and strength. If field lines crossed, it would imply two different field directions at the same point, which is physically impossible. When you place multiple sources, the pink arrows and gold streamlines follow the vector sum of the individual fields, so the net pattern stays non-crossing.

How is the strength of the field represented in the visualization?

Relative |B| is shown mainly by the pink arrow grid: longer and more opaque arrows mean a stronger field. Gold curves are a fixed set of streamlines seeded near each magnet’s poles to suggest N↔S paths — their spacing is not a quantitative |B| map. Near wires and poles the arrows grow quickly because the model fields diverge as 1/r or 1/r³.

Does the simulator show the magnetic field inside the magnet?

No. Magnets are treated as point dipoles for the exterior field only. A real bar magnet has an interior field from south to north that closes the loop; that interior region is omitted here for clarity, so gold lines stop near the dipole rather than continuing through the magnet.

Magnetic Field

Bar magnets and current-carrying wires with field line visualization.

About this model

This simulator visualizes magnetic fields from two classroom sources: bar magnets and straight current-carrying wires. Wires make circular fields given by the right-hand rule, while magnets are drawn as point dipoles with streamlines suggesting N↔S paths outside the magnet. Add and move sources to see superposition and how current, distance, and orientation shape B.

Who it's for: High school and introductory undergraduate physics students studying electromagnetism, particularly those learning about magnetic fields, the right-hand rule, and field superposition.

Key terms

Magnetic Field
Biot-Savart Law
Ampere's Law
Right-Hand Rule
Field Lines
Magnetic Dipole
Permeability of Free Space (μ₀)
Superposition Principle

How it works

Magnetic dipoles are modeled as point dipoles (field ∝ 1/r³). Long straight wires produce the familiar 1/r circular field in the plane (right-hand rule). Pink arrows show local B direction with length/opacity indicating relative |B|; gold curves are field-line streamlines traced from both the north and south sides of each magnet (suggesting N↔S paths). External field only — no interior magnet model.

Key equations

Dipole (sketch): B ∝ 3(m·r̂)r̂ − m over |r|³

Long wire: |B| ∝ |I|/r, tangent to circles (right-hand rule)

Frequently asked questions

Why are the field lines around a wire circles, but they curve between the poles of a magnet?: The geometry of the source dictates the field shape. A long, straight wire has a symmetrical cylindrical geometry, so the field lines form concentric circles around it. A bar magnet is a dipole, with a north and south pole; outside the magnet, field lines leave the north pole and enter the south pole, creating the characteristic curved arcs. Both patterns are solutions to the fundamental magnetic field equations for their respective source geometries.
Can magnetic field lines ever cross?: No. At any point in space, the magnetic field has a single, unique direction and strength. If field lines crossed, it would imply two different field directions at the same point, which is physically impossible. When you place multiple sources, the pink arrows and gold streamlines follow the vector sum of the individual fields, so the net pattern stays non-crossing.
How is the strength of the field represented in the visualization?: Relative |B| is shown mainly by the pink arrow grid: longer and more opaque arrows mean a stronger field. Gold curves are a fixed set of streamlines seeded near each magnet’s poles to suggest N↔S paths — their spacing is not a quantitative |B| map. Near wires and poles the arrows grow quickly because the model fields diverge as 1/r or 1/r³.
Does the simulator show the magnetic field inside the magnet?: No. Magnets are treated as point dipoles for the exterior field only. A real bar magnet has an interior field from south to north that closes the loop; that interior region is omitted here for clarity, so gold lines stop near the dipole rather than continuing through the magnet.

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