Lorentz Force
Shoot charges through B-field. Builds on Coulomb's Law.
A positive charge is moving horizontally to the right. It enters a region where a uniform magnetic field points straight into the screen (toward you). The charge has no electric field acting on it — only the magnetic field is present.
What happens to the moving charge?
The charge curves into a perfect circle! The magnetic force (F = qv × B) is always perpendicular to the velocity, so it acts as a centripetal force. It changes the direction of motion but never the speed — the kinetic energy stays constant throughout.
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Watch the force arrow — it always points perpendicular to the velocity. Try flipping the B-field direction or the charge sign to see how the circular path reverses.
F = qv × B
The cross product means the force is perpendicular to both v and B. It changes direction, never speed. The radius of the circular orbit is r = mv/(qB).
Charged particles from the solar wind spiral along Earth’s magnetic field lines, guided by the Lorentz force toward the poles, where they collide with atmospheric molecules and create dazzling light shows.
Old TVs steered an electron beam using magnetic fields. Deflection coils applied the Lorentz force to sweep the beam across the screen, painting each frame line by line.
Scientists sort atoms by mass using the Lorentz force. Different masses curve at different radii in a magnetic field (r = mv/qB), allowing precise identification of isotopes and molecules.
At CERN and other labs, powerful magnets use the Lorentz force to bend particle beams into circular paths. The stronger the magnet, the tighter the curve — and the higher the energy you can reach.
“A force that never does work, yet bends the path of every charged particle in the universe. That’s the magnetic force: nature’s invisible steering wheel.”
Lorentz Force Lab
Fire charged particles into a magnetic field and watch them curve. Adjust the field strength, particle speed, charge, and mass to see how each affects the orbital radius. Launch multiple particles to compare their paths side by side.
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Start with default settings and watch the circular path form. Now double the speed — the radius doubles (r = mv/qB). Try doubling the B-field instead: the radius halves. Switch to a negative charge and watch the orbit reverse direction. Finally, launch two particles with different masses to see how mass affects the radius.
The Lorentz force is always perpendicular to velocity, so it does zero work and can’t change the particle’s speed. It only steers. The circular orbit radius r = mv/(qB) tells you everything: faster or heavier particles make bigger circles; stronger fields or larger charges make tighter ones.