Physics 9702 · AS & A Level · Force on a moving charge
Force on a moving charge — practice question
An electron with charge $-q$ and mass $m$ starts from rest in a vacuum and is accelerated through a potential difference $V$. It then moves into a region of uniform magnetic field of magnetic flux density $B$, as shown in Fig. 7.1. The uniform magnetic field is directed into the plane of the paper. The electron’s velocity on entry to the magnetic field is perpendicular to the field. The radius of the circular path of the electron in the magnetic field is $r$.
(a)[3]
Explain why the electron follows an arc of a circle in the magnetic field.
(b)[2]
Show that the magnitude $p$ of the momentum of the electron as it enters the magnetic field is given by $p = \sqrt{2mqV}$.
(c)[3]
The potential difference $V$ equals $120\,\text{V}$. The radius $r$ of the circular arc is $7.4\,\text{cm}$. Determine the magnitude $B$ of the magnetic flux density.
(d)[2]
The potential difference $V$ in (c) is increased. The magnetic flux density $B$ remains 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.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Magnetic force is at right angles to velocity” …