Current-generated fields, loops, and the Lorentz force
Moving charges make magnetic fields, and magnetic fields steer moving charges. Unlike electric field lines, magnetic field lines always close into loops.
Slide the current from into the page to out of it. The field circles the wire, strongest close in, and flips direction when the current reverses.
Cross-section of a current-carrying wire. The magnetic field forms concentric circles obeying the right-hand rule. Arrow brightness indicates field strength, which falls off as 1/r from the wire.
Moving charges and currents create magnetic fields. Unlike electric fields, magnetic field lines always form closed loops -- there are no magnetic monopoles. The force on a moving charge in a magnetic field is perpendicular to both the velocity and the field: F = qv × B, the Lorentz force.
A current-carrying wire creates a B-field that circles around it, following the right-hand rule. The strength falls off as B = μ₀I/(2πr).
Key insight: The circular field pattern around a wire is a direct consequence of Ampere's law. Reversing the current reverses the field direction.
Adjust the current and the loop radius, and watch the on-axis field graph. Far from the loop the field falls off as 1/z³, just like a bar magnet.
Field lines of a current loop resemble a bar magnet (magnetic dipole). The graph shows B along the axis, peaking at the center and falling off as 1/z³ far away.
A circular current loop creates a field pattern identical to a magnetic dipole -- just like a bar magnet. The field on the axis has a clean formula, and far away it falls off as 1/r³.
Key insight: All magnetism in matter comes from current loops at the atomic scale (orbiting electrons, spin). There are no fundamental magnetic charges.
Launch a + or − charge, then change its speed and the field strength B. The orbit grows or shrinks but the speed never changes; tick E-field to see the particle drift.
A charged particle in a perpendicular magnetic field follows a circular orbit (Lorentz force). Enable the E-field to see E×B drift: the particle drifts sideways while circling.
A charged particle in a uniform magnetic field follows a circular orbit. The Lorentz force F = qv × B is always perpendicular to the velocity, so it changes direction but not speed. The cyclotron radius r = mv/(qB) depends on mass, speed, charge, and field strength.
Key insight: The magnetic force does no work (it is always perpendicular to velocity). It steers particles without changing their energy. This is the principle behind cyclotrons, mass spectrometers, and the aurora.
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