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

Force on a moving charge — practice question

(a)[2]

Define magnetic flux density in terms of the force on a current-carrying conductor.

(b)[2]

Electrons, each with mass $m$ and charge $q$, are accelerated from rest in a vacuum through a potential difference $V$. Derive an expression, in terms of $m$, $q$ and $V$, for their final speed $v$. Explain your working.

(c(i))[2]

The accelerated electrons in (b) are introduced at point $S$ into a region of uniform magnetic field of flux density $B$, as shown in Fig. 8.1. The electrons travel at right angles to the direction of the magnetic field. Their path is a circle of radius $r$. Show that the specific charge $\frac{q}{m}$ of the electrons is given by the expression $\frac{q}{m} = \frac{2V}{B^2 r^2}$. Explain your working.

(c(ii))[2]

Electrons are accelerated through a potential difference $V$ of $230\,\text{V}$. The electrons are injected normally into the magnetic field of flux density $0.38\,\text{mT}$. The radius $r$ of the circular orbit of the electrons is $14\,\text{cm}$. Use this information to calculate a value for the specific charge of an electron.

(c(iii))[2]

Suggest why the arrangement outlined in (ii), using the same values of $B$ and $V$, is not practical for determining the specific charge of $\alpha$-particles.

(i)[2]

Show that the specific charge $\frac{q}{m}$ of the electrons is given by the expression $\frac{q}{m} = \frac{2V}{B^2 r^2}$. Explain your working.

(ii)[2]

Electrons are accelerated through a potential difference $V$ of $230\,\text{V}$. The electrons are injected normally into the magnetic field of flux density $0.38\,\text{mT}$. The radius $r$ of the circular orbit of the electrons is $14\,\text{cm}$. Use this information to calculate a value for the specific charge of an electron.

(iii)[2]

Suggest why the arrangement outlined in (ii), using the same values of $B$ and $V$, is not practical for determining the specific charge of $\alpha$-particles.

Worked solution & mark scheme

This 16-mark question has a full step-by-step worked solution and mark scheme. One marking point: Force on each unit length

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI