charged particles
Summary
Charged particles (electrons, protons, ions) carry net charge q, in multiples of e = 1.60 × 10⁻¹⁹ C, and feel forces in electric and magnetic fields. Most testable: the electric force qE can do work, while the magnetic force qvB sinθ is perpendicular to velocity and bends the path without changing speed.
Detail
Meaning: A charged particle has net electric charge q, such as an electron (−e), a proton (+e) or an ion. Like charges repel and opposite charges attract. In an electric field, a positive charge is pushed along the field and a negative charge opposite to it. In a magnetic field, only a moving charge feels a force, and it points perpendicular to both the velocity and the field (right-hand rule for positive charges, reversed for negative ones).
Equation: F = qE (electric force) and F = qvB sinθ (magnetic force), giving a circular path of radius r = mv/(qB); F is force in N, q is charge in C, E is electric field in N/C (V/m), v is speed in m/s, B is magnetic field in T, θ is the angle between v and B, m is mass in kg, r is radius in m.
On the MCAT: Passages describe particles in a mass spectrometer, between parallel plates, or in a velocity selector. You predict the deflection direction, compare radii (larger m or v gives larger r, larger q gives smaller r), or use qE = qvB, so v = E/B, for undeflected motion.
Common confusion: Students point the magnetic force along v or B. It is perpendicular to both, so it does no work and the speed stays constant, whereas the electric force can change kinetic energy. A particle at rest, or moving parallel to B, feels no magnetic force.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.