In AP Physics C: E&M, the kinematics of a charged particle describes its motion under electric and magnetic forces, using Newton's second law (a = qE/m in a uniform E field) plus standard kinematic equations, and circular-motion analysis (r = mv/qB) when the force comes from a magnetic field.
Kinematics of a charged particle is just your Mechanics toolkit applied to a new force. Take a particle with charge q and mass m, figure out the net force from the fields it's in, divide by m, and you have an acceleration you can feed into the same kinematic equations you used for projectiles back in Physics C: Mechanics.
There are two main cases, and they behave completely differently. In a uniform electric field, the force F = qE is constant, so a = qE/m is constant, and the particle traces a parabola. It's projectile motion with qE/m playing the role of g. In a uniform magnetic field, the force F = qv × B is always perpendicular to the velocity, so it changes the particle's direction but never its speed. That's the recipe for uniform circular motion, and setting qvB = mv²/r gives the radius r = mv/(qB). If the velocity has a component along B, that component is untouched and the path becomes a helix. When both fields are present, you add the forces as the full Lorentz force before doing any kinematics.
This term lives in Topic 12.2, Magnetism and Moving Charges, but it's really the payoff of the whole course so far. Topic 12.2 asks you to take the magnetic force on a moving charge, F_B = q(v × B), and turn it into an actual trajectory, which means combining E&M force laws with the circular motion and kinematics you mastered in Mechanics. It's one of the clearest places where the exam tests whether you can chain ideas together: field, then force, then acceleration, then motion. Velocity selectors, mass spectrometers, and cyclotron-style problems all reduce to this one skill, so it shows up constantly in both multiple choice and free response.
Keep studying AP® Physics C: E&M Unit 12
F_B = q(v × B) (Topic 12.2)
This is the force that drives the magnetic side of the kinematics. Because it's always perpendicular to v, it does zero work, so the particle's speed never changes. Only its direction does. That single fact is why charges circle in magnetic fields instead of speeding up.
Lorentz force (Topic 12.2)
The full force on a charge is F = qE + qv × B. Kinematics problems with both fields, like a velocity selector, hinge on this sum. When qE exactly cancels qvB, the particle moves in a straight line at v = E/B, which is a classic exam setup.
Cross product (Topic 12.2)
You can't predict which way the particle curves without v × B and the right-hand rule. Getting the direction wrong flips the entire trajectory, and remember that negative charges curve the opposite way from what your right hand says.
Hall effect (Topic 12.2)
The Hall effect is charged-particle kinematics inside a conductor. Moving charges get deflected sideways by qv × B, pile up on one edge, and build an electric field until qE balances the magnetic force. It's a velocity selector that builds itself.
No released FRQ uses the phrase "kinematics of charged particle" verbatim, but the underlying skill is a staple of E&M free response and multiple choice. Expect to: (1) derive a = qE/m and treat motion in a uniform E field as projectile motion, often for a charge shot between parallel plates; (2) set qvB = mv²/r to find the radius, period (T = 2πm/qB), or speed of a charge circling in a B field; (3) use the right-hand rule to determine which way the path bends, flipping for negative charges; (4) analyze crossed E and B fields and solve for the undeflected speed v = E/B. FRQs love multi-stage setups where a particle is accelerated through a potential difference first (use energy conservation, qΔV = ½mv²) and then enters a magnetic field region. Watch for the conceptual MCQ trap that magnetic forces do no work, so B fields alone can never change a particle's kinetic energy.
Both are "charged particle kinematics," but the trajectories are totally different. A uniform E field exerts a constant force along the field, giving constant acceleration and a parabolic path, and it changes the particle's speed and kinetic energy. A uniform B field exerts a force perpendicular to velocity, giving circular (or helical) motion at constant speed, and it never changes kinetic energy because it does no work. If an exam question asks how the speed changed, the answer involves E, never B.
In a uniform electric field, a charged particle has constant acceleration a = qE/m and follows a parabolic path, exactly like projectile motion with qE/m replacing g.
In a uniform magnetic field, the force qv × B is always perpendicular to velocity, so the particle moves in a circle of radius r = mv/(qB) at constant speed.
Magnetic forces do zero work, so a magnetic field alone can never change a charged particle's speed or kinetic energy, only its direction.
In crossed E and B fields (a velocity selector), the particle travels undeflected when qE = qvB, which gives v = E/B.
If the velocity has a component parallel to B, that component is unaffected and the path is a helix, circular motion plus constant-velocity drift along the field.
Negative charges curve opposite to the right-hand rule prediction, so always check the sign of q before committing to a direction.
It's the analysis of how a charge moves under electric and magnetic forces. You compute acceleration from a = qE/m in an electric field, or set qvB = mv²/r for circular motion in a magnetic field, then apply standard kinematics from Topic 12.2.
No. The magnetic force qv × B is always perpendicular to the velocity, so it does zero work and never changes the particle's speed or kinetic energy. Only electric fields can change a charge's speed.
An E field gives a constant force and a parabolic path that changes the particle's speed, just like gravity in projectile motion. A B field gives a perpendicular force and a circular path at constant speed, with radius r = mv/(qB).
r = mv/(qB). It comes from setting the magnetic force equal to the centripetal requirement, qvB = mv²/r. Faster or more massive particles make bigger circles; stronger fields or larger charges make tighter ones.
A velocity selector uses perpendicular (crossed) E and B fields so the electric force qE and magnetic force qvB point in opposite directions. Only particles with exactly v = E/B pass through undeflected, regardless of their charge or mass.
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