Question

A proton and a deuteron are moving with equal velocities perpendicular to a uniform magnetic field. A deuteron has the same charge as the proton but has twice its mass. What is the ratio of the acceleration of the proton to that of the deuteron?

Answer 1

The ratio of the acceleration of the proton to that of the deuteron in a uniform magnetic field, when both have equal velocities, is 2:1 since the deuteron has twice the mass of the proton but they share the same charge.

Step-by-step explanation:

The question pertains to the comparison of acceleration of a proton and a deuteron when both are moving with equal velocities and subjected to a uniform magnetic field. According to the Lorentz force law, the magnetic force F on a charged particle is given by F = qvB sin(θ), where q is the charge of the particle, v is the velocity, B is the magnetic field, and θ is the angle between the velocity and the magnetic field. Since θ is 90 degrees (perpendicular movement), sin(θ) is 1, and the force exerted on both particles is F = qvB. However, acceleration a is F/m, where m is the mass of the particle. With the proton and deuteron having the same charge but the deuteron having twice the mass, the proton's acceleration would be twice that of the deuteron. Therefore, the ratio of the acceleration of the proton to that of the deuteron is 2:1.