What this model teaches
Magnetic fields do not begin on positive charges and end on negative charges: magnetic field lines form continuous loops. This page connects the right-hand rule, Biot–Savart law, Ampère’s law, superposition and Lorentz force in one visual model.
Biot–SavartAmpèreRight-hand ruleSuperpositionSolenoidHelmholtzMagnetic dipoleLorentz force
Choose a magnetic-field sourcethe field map and equations update together
Source & display controls
Current source
Long straight conductor normal to the pageVisualization layers
Moving test charge at probe
This test charge does not modify the source field. It is used only to visualize F = qv × B.
Probe & source results
Interactive magnetic field map
Drag the white probe anywhere in the field. Current symbols use ⊙ for current out of the page and ⊗ for current into the page. Moving particles follow the conventional magnetic-field direction.
drag probe · ⊙ current out · ⊗ current in · blue = magnetic field · orange = Lorentz force
magnetic field line• current out of page× current into pagewhite crosshair = probe
Centerline field profile
|B| sampled along y = 0 through the displayed domainHow to read a magnetic-field picture
Different visual layers answer different questions. Use the probe for quantitative values; use the field map to understand geometry and direction.
01 / Field vectorsEach arrow is tangent to B and points in the direction a compass north pole would point. Arrow length is log-scaled for readability.
02 / Field linesMagnetic field lines are continuous: they do not start or stop at isolated magnetic charges. The model traces them numerically through B.
03 / Magnitude shadingThe blue wash highlights strong-field regions using a logarithmic display scale. It is visual support, not a separate physical quantity.
04 / Lorentz forceThe orange probe arrow uses F = qv × B for a test particle moving normal to the page. Reversing q or v reverses the force.
Model assumptions & limits
The page is designed for education and preliminary checks, not detailed electromagnetic design of real equipment.
Calculations use μ = μ₀. Ordinary air is close to μᵣ = 1. Ferromagnetic cores, saturation, hysteresis and nonlinear permeability are not modeled.
Circular loops are integrated from the Biot–Savart law using finite line segments. A finite solenoid is represented by distributed circular turns. Analytical center/on-axis relations are shown alongside the numerical field as validation anchors.
Field lines are streamlines traced through the calculated vector field. Their count and spacing are selected for clarity and are not a calibrated magnetic-flux scale.
The bar-magnet view uses an ideal magnetic dipole moment. It reproduces the far field well but is not a finite-element model of a real permanent magnet, especially close to or inside the drawn magnet body.
Background & FAQ
Classical magnetostatics satisfies ∇·B = 0: there is no observed isolated magnetic charge in the model. Field lines therefore continue through space and through magnetic material rather than terminating at a north or south pole.
For a straight conductor, point your right thumb with conventional current; curled fingers give the direction of B. For a current loop, curl your fingers with current and the thumb gives the loop magnetic-moment / central-field direction.
Ampère’s law is always true, but it becomes a simple algebraic tool only when symmetry makes B constant or otherwise easy to handle along a chosen integration path. Biot–Savart is more directly useful for finite loops and less symmetric current distributions.
For two identical coaxial coils, spacing them by one coil radius makes the second derivative of the axial field vanish at the midpoint. The central region therefore has unusually small field curvature and is useful when a nearly uniform magnetic field is desired.
No. The magnetic part of the Lorentz force is qv × B, so it is zero when the particle velocity is zero. Magnetic force is also perpendicular to instantaneous velocity, so an ideal magnetic field changes direction of motion rather than doing mechanical work on a point charge.
B is magnetic flux density, measured in tesla. H is magnetic field strength, measured in A/m. In vacuum B = μ₀H. In magnetic materials the relation depends on magnetization and may be nonlinear; this page models B directly in μᵣ ≈ 1 media.