A proton moves in the +x direction through a region where the magnetic field points in the +x direction. What magnetic force does the proton experience?
AA force in the +y direction, perpendicular to the proton's motion
BA force in the −x direction, opposing the proton's motion
CNo magnetic force, because the velocity and field are parallel
DA force whose direction depends on the proton's speed
The magnetic force is F = q(v × B). When v and B are parallel (both in the +x direction), their cross product is zero: v × B = 0. The magnetic force is identically zero for any charge moving parallel to the field, regardless of speed or charge magnitude. Only the component of velocity perpendicular to B contributes to the force. This is why particles moving parallel to a magnetic field are undeflected — a key geometric property of the Lorentz force.
Question 2 Multiple Choice
A proton moves perpendicular to a uniform magnetic field, undergoing circular motion with orbital radius r. If the magnetic field strength is doubled while the proton's speed remains constant, what happens to the orbital radius?
AThe radius doubles, because stronger fields create larger orbits
BThe radius halves, because r = mv/(qB) and B appears in the denominator
CThe radius stays the same, because the speed is unchanged
DThe radius increases by √2, because force scales with the square root of field strength
From the circular motion condition mv²/r = qvB, solving for r gives r = mv/(qB). The radius is inversely proportional to B — doubling the field strength halves the radius. A stronger field exerts a larger centripetal force, curving the path more tightly. This relationship is the operating principle of mass spectrometers: ions of different mass but same charge and speed follow different radii, allowing separation by mass-to-charge ratio.
Question 3 True / False
The magnetic force on a moving charge can change the charge's direction of motion without changing its kinetic energy.
TTrue
FFalse
Answer: True
The magnetic force F = q(v × B) is always perpendicular to the velocity v by the definition of the cross product. Since work = F · d, and force is always perpendicular to displacement, the work done by the magnetic force is always zero. Zero work means no change in kinetic energy, and therefore no change in speed. The magnetic force is a pure steering force — it redirects without accelerating or decelerating. This is why a charged particle in a uniform perpendicular field moves in a circle at constant speed.
Question 4 True / False
Doubling the strength of a magnetic field causes a charged particle moving in a circular orbit to speed up, because the particle experiences a stronger force.
TTrue
FFalse
Answer: False
The magnetic force never changes a particle's speed — it can only change direction. Even though a stronger field exerts a larger force and curves the path more tightly (smaller radius), the force remains perpendicular to velocity at every instant and does zero work. The particle moves faster around a tighter circle in the same amount of time — specifically, the orbital period T = 2πm/(qB) decreases with stronger field, but the speed v = qBr/m stays determined by initial conditions, not field strength.
Question 5 Short Answer
Why does the magnetic force F = q(v × B) do no work on a moving charge, and what consequence does this have for how the charge moves?
Think about your answer, then reveal below.
Model answer: The cross product v × B is always perpendicular to v. Since the force is perpendicular to the velocity (and thus to the displacement at every instant), the dot product F · v = 0, meaning the rate of work done is identically zero. Zero work means no change in kinetic energy and therefore no change in speed. The consequence is that the magnetic force can only steer — it changes the direction of motion but not the magnitude. A charged particle moving perpendicular to a uniform field follows uniform circular motion: constant speed, changing direction.
This is the most important conceptual point about magnetic forces: unlike electric forces, which can accelerate and decelerate charges, magnetic forces are purely geometric — they act as a compass that redirects the particle without adding or removing energy. This is why magnetic confinement in particle accelerators and plasma reactors can steer high-energy beams without changing their energy, and why the aurora borealis forms as solar wind particles are funneled along magnetic field lines toward the poles without being slowed down.