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.The ratio of the acceleration of the proton to that of the deuteron is:
A)0.5.
B)1.
C)2.
D)There is no acceleration in this case.

Question

Quizplus · Accepted Answer

The acceleration $a$ of a charged particle in a magnetic field is given by $a = \frac{F}{m}$, where $F = qvB$ is the magnetic force, $q$ is the charge, $v$ is the velocity, $B$ is the magnetic field strength, and $m$ is the mass of the particle. Since both the proton and the deuteron have the same charge and are moving with the same velocity in the magnetic field, the force $F$ on both particles is the same. However, the deuteron has twice the mass of the proton ($m_{deuteron} = 2m_{proton}$). Therefore, the acceleration of the proton is twice that of the deuteron, making the ratio of the acceleration of the proton to that of the deuteron $2:1$ or simply $2$.

A Proton and a Deuteron Are Moving with Equal Velocities