Question

A charged particle is moving in a constant magnetic field. Which of the following statements concerning the magnetic force exerted on the particle is (are) true? (Assume that the magnetic field is not parallel or antiparallel to the velocity.) a) It does no work on the particle. b) It may increase the speed of the particle. c) It may change the velocity of the particle. d) It can act only on the particle while the particle is in motion. e) It does not change the kinetic energy of the particle.

Short answer

Answer: The true statements about the magnetic force exerted on a charged particle moving in a constant magnetic field are a), c), d), and e).

Step-by-step solution

Statement a) It does no work on the particle.

The work done by a force on a particle is given by the dot product of the force vector and the displacement vector. The magnetic force, also known as the Lorentz force, acting on a charged particle is given by F = q(v × B), where F is the magnetic force vector, q is the charge of the particle, v is the velocity vector of the particle, and B is the magnetic field vector. Since the cross product (v × B) is always perpendicular to both v and B, the magnetic force is always perpendicular to the displacement of the particle, hence the dot product is zero, and no work is done on the particle. So, statement a) is true.

Statement b) It may increase the speed of the particle.

Since the magnetic force does no work on the particle, as we established in statement a), it cannot change the kinetic energy of the particle, which implies it cannot change the speed of the particle. So, statement b) is false.

Statement c) It may change the velocity of the particle.

Although the magnetic force does not change the speed of the particle, as stated in statement b), it can still change the direction of the velocity vector. Since velocity is a vector quantity with both magnitude and direction, a change in the direction of the velocity vector implies a change in velocity. Therefore, statement c) is true.

Statement d) It can act only on the particle while the particle is in motion.

The magnetic force experienced by a charged particle is given by F = q(v × B), which implies that the force depends on the velocity of the particle. If the particle is stationary, its velocity is zero, and the magnetic force will be zero as well. Thus, the magnetic force can act only on the particle while the particle is in motion. So, statement d) is true.

Statement e) It does not change the kinetic energy of the particle.

We have already established in statement a) that the magnetic force does no work on the particle. Since work is related to the change in kinetic energy by the work-energy theorem, and no work is done by the magnetic force, it does not change the kinetic energy of the particle. Hence, statement e) is true. In conclusion, the true statements about the magnetic force exerted on a charged particle moving in a constant magnetic field are a), c), d), and e).