Magnetic force is the force on a moving charged particle in a magnetic field, given by F = qv × B (or F = IL × B for a current-carrying wire). It points perpendicular to both the velocity and the field, has magnitude qvB sin θ, and does no work on the charge because it never points along the motion.
Magnetic force is what a magnetic field does to moving charge. For a single particle it's the magnetic part of the Lorentz force, F = qv × B, with magnitude qvB sin θ. For a wire carrying current I over a length L in a field, the same physics becomes F = IL × B. Either way, the direction comes from the cross product, so the force is always perpendicular to both the velocity (or current) and the field. You find that direction with the right-hand rule, and you flip it for negative charges.
That perpendicular direction is the whole personality of this force. Because it never points along the motion, the magnetic force does zero work and can never change a particle's speed or kinetic energy. All it can do is steer. A charge moving perpendicular to a uniform field gets bent into a circle, with the magnetic force acting as the centripetal force. If the velocity is parallel to B, sin θ = 0 and the force vanishes entirely. A stationary charge feels nothing at all.
Magnetic force is the backbone of the magnetism portion of AP Physics C: E&M. It's the bridge concept that connects magnetic fields (which you calculate with Biot-Savart and Ampère's law) back to actual motion and Newton's second law. It shows up in charged-particle problems (circular and helical motion, velocity selectors, mass spectrometers), in force-on-a-wire problems (forces between parallel currents, torque on loops), and again in electromagnetic induction, where the magnetic force on charges in a moving conductor is what produces motional EMF. If you can't fire off F = qv × B with the correct direction, most of the second half of the course falls apart. It's also a favorite way for the exam to mix in Mechanics, since setting qvB = mv²/r is a Newton's-second-law problem wearing an E&M costume.
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Lorentz Force Law (Unit 4)
Magnetic force is half of the full Lorentz force, F = qE + qv × B. When both fields are present, like in a velocity selector, the electric force can push while the magnetic force steers, and balancing them gives v = E/B.
Right-hand Rule for Cross Products (Unit 4)
The direction of magnetic force is pure cross product. Point your fingers along v (or the current), curl toward B, and your thumb gives F for a positive charge. Negative charge? Reverse it. Most lost points on magnetism FRQs are direction errors, not algebra errors.
Centripetal Motion (Mechanics, Unit 1)
Because magnetic force is always perpendicular to velocity, it's a perfect centripetal force. Setting qvB = mv²/r gives r = mv/(qB), the workhorse equation for every charged-particle-in-a-field problem on the exam.
Electromagnetic Waves (Unit 5)
Induction problems run on magnetic force too. When a conducting rod slides through a field, the magnetic force qv × B on the charges inside it drives current, producing motional EMF. That same E-and-B interplay, pushed further, is what makes electromagnetic waves possible.
Magnetic force is tested both as a quick MCQ direction check ("which way does the force point on this charge or wire?") and as a full FRQ workhorse. The 2025 FRQ asked about two long parallel wires carrying opposite currents, where each wire's field exerts a force on the other, and opposite currents repel. The 2023 FRQ put a conducting rod on rails attached to a spring, combining the magnetic force on a current-carrying rod (F = ILB) with motional EMF and circuit analysis. Expect to (1) compute magnitudes with qvB sin θ or BIL, (2) nail directions with the right-hand rule and justify them in words, (3) set the magnetic force equal to mv²/r for circular motion, and (4) explain why the force does no work on a moving charge. Direction justifications are graded explicitly, so practice writing them out, not just drawing arrows.
Electric force (qE) acts on any charge, moving or not, points along the field line, and can do work to speed a charge up. Magnetic force (qv × B) only acts on moving charges, points perpendicular to both v and B, and does zero work, so it changes direction but never speed. A velocity selector works precisely because these two forces can cancel each other.
Magnetic force on a moving charge is F = qv × B with magnitude qvB sin θ, and on a current-carrying wire it's F = IL × B.
The force is always perpendicular to the velocity, so it does zero work and can change a particle's direction but never its speed or kinetic energy.
Use the right-hand rule to find the force direction for positive charges, and reverse the result for negative charges.
A charge moving perpendicular to a uniform field travels in a circle, and setting qvB = mv²/r gives the radius r = mv/(qB).
There is no magnetic force on a stationary charge or on a charge moving parallel to the field, since sin θ = 0 in both cases.
Parallel wires carrying currents exert magnetic forces on each other, attracting when currents run the same way and repelling when they're opposite.
It's the force a magnetic field exerts on moving charge, given by F = qv × B for a particle and F = IL × B for a current-carrying wire. It points perpendicular to both the velocity (or current) and the field, with magnitude qvB sin θ.
No. The magnetic force is always perpendicular to the particle's velocity, so the work done is zero. It can bend the path into a circle, but the speed and kinetic energy never change. This "why" question is a classic exam justification.
Electric force qE acts on any charge, even one at rest, and points along the field. Magnetic force qv × B only acts on moving charges, points perpendicular to both v and B, and does no work. In a velocity selector the two cancel when v = E/B.
No. Since F = qv × B, if v = 0 the force is zero. The same is true if the charge moves parallel to the field, because sin θ = 0. Only the velocity component perpendicular to B produces a force.
Recent FRQs have used it heavily. The 2025 exam featured forces between long parallel wires carrying opposite currents, and the 2023 exam combined F = ILB on a rod with motional EMF in a rails-and-spring circuit. You'll typically compute a magnitude, justify a direction with the right-hand rule, or set qvB equal to mv²/r.
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