Question

How does the magnetic force on a stationary charged particle compare to the magnetic force on a moving charged particle? A. There is no magnetic force on a moving charged particle. B. There is no magnetic force on a stationary charged particle. C. The force on a moving particle is multiplied by the magnitude of the velocity. D. The force on a moving particle is twice the force on an identical stationary particle.

Answer 1

B is the most correct. This comes from Lorentz's Force Law: F = q(E+ v x B), where F is force, q is charge, E is the magnitude of the electric field, v is the velocity of the particle and B is the magnitude of the magnetic field. If we examine the v x B term (this is the only term the magnetic field contributes to), we know that the cross product will equal zero if v is zero (if the charge is stationary). If you're not terribly comfortable with cross products, change v x B into v*B*sinθ, where θ is the angle between the v and B vectors. This simplification also forces you to use the right hand rule to find the resulting direction of the cross product, but makes the math more straight forward. A is incorrect because ALL charged particles create magnetic fields that also exercise force on the particle. For C, while the force does get bigger with higher velocity, it isn't straightly multiplied, more closely it multiples the magnetic field, B, and that generates more force, but even then we only purely multiply v and B when the angle between them (θ) is 90°, so sinθ = 1 and that term disappears. D is wrong because the magnetic force on a stationary charged particle is zero, always, and when it is moving it is non-zero.