The Lorentz force is the total electromagnetic force on a charged particle, F = qE + q(v × B), combining the electric force qE with the magnetic force qv × B; for a current-carrying wire, the magnetic part becomes F = IL × B. It appears in Topic 12.2, Magnetism and Moving Charges.
The Lorentz force is the complete answer to the question "what force does a charged particle feel from electromagnetic fields?" Written out, it's F = qE + q(v × B). The first piece, qE, is the electric force you've used since Unit 8. The second piece, q(v × B), is the magnetic force, and it only shows up when the charge is moving. A stationary charge in a pure magnetic field feels nothing.
The magnetic part has personality. Because it's a cross product, the force is always perpendicular to both the velocity and the field, its magnitude is qvB sin θ, and its direction comes from the right-hand rule (flipped for negative charges like electrons). That perpendicularity has a huge consequence. The magnetic force can never do work on a charge, so it changes the direction of motion but never the speed. For a current-carrying wire, the same physics scales up to F = IL × B, since a current is just a stream of moving charges.
The Lorentz force lives in Topic 12.2, Magnetism and Moving Charges, and it's the bridge between everything you learned about electric fields earlier in the course and the magnetism content that closes it out. It explains why charges spiral or circle in magnetic fields, why current-carrying wires feel forces, and why a velocity selector lets only one speed of particle pass straight through (the spot where qE exactly cancels qvB). It's also the conceptual seed of the Hall effect and motional EMF. Whenever a problem says "a charge moves through both an electric and a magnetic field," the Lorentz force equation is the move.
Keep studying AP® Physics C: E&M Unit 12
F_B = q(v × B) (Topic 12.2)
This is the magnetic half of the Lorentz force. The full Lorentz force just bolts qE onto it, so if you can compute qv × B, you're one vector addition away from the complete force.
Cross product (Topic 12.2)
The magnetic term is a literal cross product, so direction-finding is half the problem. Compute v × B component by component or use the right-hand rule, then remember a negative charge flips the answer.
Kinematics of charged particles (Topic 12.2)
Once you have the Lorentz force, Newton's second law takes over. A pure magnetic force perpendicular to v produces uniform circular motion with r = mv/(qB), and adding a velocity component along B turns the circle into a helix.
Hall effect (Topic 12.2)
The Hall effect is the Lorentz force at equilibrium inside a conductor. Moving charges get pushed sideways by qv × B until the resulting charge buildup creates an electric force qE that cancels it, which is the same balance trick a velocity selector uses.
Multiple-choice questions love handing you E, B, and v as vectors with î, ĵ, k̂ components and asking for the magnitude or direction of the net force. The drill is always the same. Compute q(v × B) carefully, add qE as a vector, and watch the sign if the particle is an electron. Conceptual stems test whether you know the magnetic force vanishes for stationary charges or motion parallel to B, and that the force on an electron points opposite to what the right-hand rule gives. On free-response, the Lorentz force usually launches a longer problem, like deriving the radius of circular motion, setting up a velocity selector condition (qE = qvB), or finding the force per length on a wire with F = IL × B. Show the cross product setup explicitly; that's where the points are.
Strictly, the Lorentz force is the full sum qE + q(v × B), though textbooks (and casual exam talk) often use "Lorentz force" for just the magnetic term. The distinction matters on problems with both fields present. If you compute only qv × B and ignore qE, you get the wrong net force. When a question gives you both E and B, always add both contributions as vectors.
The full Lorentz force on a charge is F = qE + q(v × B), the electric force plus the magnetic force added as vectors.
The magnetic part is always perpendicular to the velocity, so it does zero work and changes a particle's direction but never its speed.
A charge feels no magnetic force if it's stationary or moving parallel to B, since the cross product gives qvB sin θ.
For negative charges like electrons, the force points opposite to the right-hand rule direction, which is the most common sign trap on the exam.
For a current-carrying wire, the Lorentz force becomes F = IL × B, the same physics applied to many charges flowing together.
A velocity selector works by balancing the two halves of the Lorentz force, letting through only particles with v = E/B.
It's the total electromagnetic force on a charged particle, F = qE + q(v × B), tested in Topic 12.2. The qE term is the electric force and the q(v × B) term is the magnetic force, which only acts on moving charges.
Not exactly. The magnetic force q(v × B) is only one piece of the Lorentz force, which also includes the electric force qE. If a problem has both E and B fields, you have to add both terms as vectors.
The magnetic part never can, because it's always perpendicular to the velocity, so it changes direction but not speed or kinetic energy. The electric part qE absolutely can do work, which is why accelerators use electric fields to speed particles up and magnetic fields to steer them.
Compute v × B with the right-hand rule (or component by component for î, ĵ, k̂ vectors), then flip the result because the electron's charge is negative. The electric force on an electron also points opposite to E for the same reason.
They're the same physics at different scales. F = qv × B is the magnetic force on one moving charge, while F = IL × B is that force summed over all the charges flowing through a wire of length L carrying current I.
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