Physics 9702 · AS & A Level · Force on a moving charge
Force on a moving charge — practice question
An electron with charge $-q$ and mass $m$ is accelerated from rest in a vacuum by a potential difference $V$. It then enters a region where the magnetic flux density is a uniform $B$, as shown in Fig. 7.1. The uniform magnetic field points into the plane of the paper. On entering the magnetic field, the velocity of the electron is normal to the magnetic field. The radius of the circular path followed by the electron in the magnetic field is $r$.
(a)[3]
Explain why the electron follows a circular arc in the magnetic field.
(b)[2]
Show that the magnitude $p$ of the electron’s momentum as it enters the magnetic field is $p = \sqrt{2mqV}$.
(c)[3]
The potential difference $V$ in (c) is increased. The magnetic flux density $B$ stays unchanged. Using the momentum of the electron, explain the effect of this increase on the radius $r$ of the electron’s path in the magnetic field.
(d)[2]
In (c), the potential difference $V$ is increased, while the magnetic flux density $B$ remains unchanged. Referring to the momentum of the electron, explain how this increase affects the radius $r$ of the electron’s path in the magnetic field.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “magnetic force acting at right angles to velocity” …