Physics 2 · Unit 5: Magnetism and Electromagnetic Induction · 14 min read · Updated 2026-05-11
Force on Moving Charges in Magnetic Fields — AP Physics 2
AP Physics 2 · Unit 5: Magnetism and Electromagnetic Induction · 14 min read
1. The Magnetic Lorentz Force Law: Magnitude and Direction★★☆☆☆⏱ 4 min
When a moving electric charge travels through an external magnetic field, the field exerts a magnetic force on the charge. Unlike electric force (which acts on charges regardless of motion) and gravitational force (negligible for subatomic particles), magnetic force is always perpendicular to both the velocity of the charge and the magnetic field vector, so it never does work on a moving charge.
For direction, use the right-hand rule: point the fingers of your right hand along $\vec{v}$, curl your fingers towards $\vec{B}$, and your thumb points in the direction of $\vec{F}_B$ for a positive charge. For negative charges, the force points in the opposite direction.
Exam tip: Always confirm the sign of the charge before reporting direction. If the problem gives an electron or other negative particle, explicitly reverse the direction you get from the right-hand rule—this is the most frequent direction error on AP MCQs.
2. Uniform Circular Motion of Charges in Uniform Magnetic Fields★★★☆☆⏱ 4 min
When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force is always perpendicular to the particle's velocity, so it acts as a centripetal force that causes the particle to move in a uniform circular path. This is one of the most commonly tested problem types on the AP Physics 2 exam.
Exam tip: Do not forget to cancel $v$ when deriving the radius formula. Leaving $v^2$ in your final expression for $r$ is a common algebra error that will cost you points on FRQs.
3. Velocity Selection in Crossed Fields★★★☆☆⏱ 3 min
A velocity selector is a common device that uses crossed electric and magnetic fields (E perpendicular to B) to filter out all particles except those moving at a specific desired speed, regardless of their mass or charge. This is the core principle behind mass spectrometry, used to identify the mass of unknown particles.
Exam tip: Even if the problem gives you the charge and mass of the particles, do not include them in your calculation of the undeflected speed. They are almost always red herrings designed to test if you know q cancels out.
4. AP-Style Practice Problems★★★★☆⏱ 3 min
Common Pitfalls
Why: Students memorize the rule for positive charges and forget that the negative sign of charge reverses the cross product direction.
Why: Students stop after equating force to centripetal force and forget to simplify.
Why: Students memorize work as force times distance and forget the direction property of magnetic force.
Why: Problems often give charge to test for this mistake, so students assume it must be used.
Why: Most AP problems use $\theta=90^\circ$, so students get used to dropping $\sin\theta$.