Electronics Engineering (ELEX) Board Practice Exam

When a proton and an alpha particle are traveling perpendicular to a magnetic field, the ratio of their speeds can be expressed as:

1. 1

2. 2

3. 4

4. 0.5

The correct answer is: 2

To determine the ratio of speeds between a proton and an alpha particle when both are moving perpendicular to a magnetic field, it's essential to understand the forces acting on charged particles in magnetic fields. The magnetic force experienced by a charged particle is given by the equation: \[ F = qvB \] where \( F \) is the magnetic force, \( q \) is the charge of the particle, \( v \) is the speed of the particle, and \( B \) is the strength of the magnetic field. For a proton, which has a charge of \( +1e \) (where \( e \) is the charge of an electron), the force is proportional to its speed. An alpha particle consists of 2 protons and 2 neutrons, giving it a total charge of \( +2e \) and a mass that is approximately four times that of a proton due to the presence of the two additional neutrons and the two protons. Since both particles are subjected to the same magnetic field, the resulting centripetal force acting on them must be equal to the magnetic force acting on each. Assuming they are accelerated to the point where their electric and magnetic forces balance (in the context of motion in the