Answer to Question #120418 in Electricity and Magnetism for Aayush

Question

A beam consisting of a mixture of two positive ions of different masses pass rightward through a magnetic field pointing out of the plane of the page, and impinge on a screen placed to the right. The screen shows two dots placed one below the other. Which dot corresponds to the heavier ion and why?

Answer 1

When charged particles move perpendicularly to the magnetic field lines, they experience the action of two forces: Lorenz's force and centripetal force. They are in equilibrium if the particles move with constant speed:

$$qvB=\frac{mv^2}{R}.$$

The dots on the screen represent the radius of a particle's orbit. Express it from the previous equation:

$$R=\frac{mv}{qB}.$$

Therefore, the higher the mass - the larger the radius. The dot that is further from the center represent heavier particle.