Physics 9702 · AS & A Level · Force on a moving charge

Force on a moving charge — practice question

A particle of mass $m$ carrying charge $-q$ moves through a vacuum with speed $v$. It then enters a uniform magnetic field with flux density $B$. The angle between the particle’s initial direction of travel and the magnetic field direction is $90^\circ$.
(a)[3]

Explain why the particle moves along an arc of a circle in the magnetic field.

(b)[1]

The radius of the arc in (a) is $r$. Show that the particle’s ratio $\frac{q}{m}$ is given by $\frac{q}{m} = \frac{v}{Br}$.

(c(i))[2]

Use these values to find the ratio $\frac{q}{m}$. The particle’s initial speed $v$ is $2.0 \times 10^7\,\text{m s}^{-1}$. The magnetic flux density $B$ is $2.5 \times 10^{-3}\,\text{T}$. The radius $r$ of the arc in the magnetic field is $4.5\,\text{cm}$. State your answer in $\text{C kg}^{-1}$.

(c(ii))[2]

The route of the negatively-charged particle before it enters the magnetic field is shown in Fig. 6.1. The magnetic field is directed into the plane of the paper. On Fig. 6.1, sketch the path of the particle in the magnetic field and after it leaves the field.

(ii)[2]

On Fig. 6.1, sketch the path of the particle in the magnetic field and after it leaves the field.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: The magnetic force has constant magnitude and acts at right angles to the motion

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