The two particles making circular paths in the magnetic field shown have the same mass and kinetic energy.The field is downward into the page.Which of the following statements concerning the particles is correct?

Question

Quizplus · Accepted Answer

The radius of the circular path of a charged particle in a magnetic field is given by r = mv/qB, where m is the mass of the particle, v is its velocity, q is its charge, and B is the strength of the magnetic field. Since the particles have the same mass and kinetic energy, their velocities and hence their radii of the circular path must be the same. From the right-hand rule, we can see that the particle with the path going clockwise must have a charge opposite in sign to that of the particle with the counterclockwise path. Therefore, q₁ and q₂ have opposite sign, and the magnitude of the charge on the particle with the smaller radius must be greater than that of the particle with the larger radius in order for their magnetic forces to balance. Hence, |q₁| < |q₂|. Therefore, the correct choice is (D).

The Two Particles Making Circular Paths in the Magnetic Field