Electricity & Magnetism · AP Physics C (Magnetism)
Lorentz Force & Charged Particle Motion Simulator
Key exam takeaway: Lorentz force is perpendicular to velocity and does ZERO work! The orbital period T = 2πm/qB is independent of velocity and radius, powering cyclotron resonance.
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3D Simulation Stage● 60 FPS
Parameter Controls
×10⁶ m/s
T
Live Derivations & Metrics
Orbit Radius r
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Cyclotron Period T
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Lorentz Force Magnitude
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Deflection Sense
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Proton (m=1.67*10^-27kg, q=1.6*10^-19C) enters B=0.1T at v=10^6 m/s. Find orbit radius and period.
Step-by-Step Derivation:
- r = mv/(qB) = 10.4cm. Period T = 2πm/(qB) = 0.656 μs.
Worked Problem
Problem: Why does the Lorentz force do zero work on moving charges? Can it change particle velocity?
Step-by-Step Derivation:
- Force f = q(v x B) is always strictly perpendicular to velocity (cos 90° = 0), doing zero work. It alters velocity direction, not speed.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: When applying the Left-Hand Rule for negative charges (electrons), which direction must the 4 fingers point?
Answer Key: Opposite to electron velocity (along conventional current direction). Thumb then points to the true force vector.
Q2. Variant 2: What dictates max kinetic energy in a cyclotron? Increase accelerating voltage U or Dees radius R?
Answer Key: Ek,max = q²B²R²/(2m). Max energy depends strictly on B and Dee radius R, independent of accelerating voltage U.
Q3. Variant 3: What two stages comprise a mass spectrometer? How does it resolve chemical isotopes?
Answer Key: Velocity selector (v = E/B) + deflection magnetic chamber. Equal-speed isotopes trace radius r = mv/(qB) proportional to atomic mass m.
Frequently Asked Questions & Misconceptions
How to remember when to use the Left Hand vs Right Hand rule in electromagnetism?
Rule of thumb: "Force = Left Hand, Electricity Generation = Right Hand". Use left hand for forces (Ampere, Lorentz); right hand for induced currents.
If a charged particle travels parallel to magnetic field lines, does it experience a Lorentz force?
Zero force! f = qvB*sin(0°) = 0. The particle continues in an unperturbed straight line at constant velocity.
What spatial trajectory results if a charge enters a magnetic field at an oblique angle θ?
A helical helix orbit! The parallel velocity component drives uniform translation while perpendicular component traces circular orbits.
How does the geomagnetic field shield Earth from solar wind? How are auroras formed?
The magnetosphere deflects lethal solar cosmic particles via Lorentz forces, channeling them down polar lines to excite atmospheric atoms into glowing auroras.