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Thomson passed electrons through a region having mutually perpendicular electric and magnetic field, and both perpendicular to the velocity of the electrons. The fields were adjusted so as to produce no deflection. This enebled him to measure the \(e/m\) of electrons.
In another scheme of measurement of \(e/m\), a charged particle is passed through a region having both electric and magnetic fields as shown in Fig 1 . An upward force due to the electric field, $eE$, is balanced by a downward magnetic force $evB$, producing no deflection if $eE=evB$. This experiment proceeds as follows.
- At first the electric and magnetic field are switched of and the undeflected position is noted .
- Next an electric field $E$ is applied and the deflection \(y\) on the screen is noted. This deflection is given by $$ y=\frac{eEl^2}{2mv^2}\Longrightarrow \frac{e}{m}=\frac{2yv^2}{ l^2}. $$
- Next a magnetic field is applied perpendicular to the electric field and its direction and magnitude is chosen so as to cancel the deflection. Using \(v= E/B\), we have \begin{align*} \frac{e}{m} =&\frac{2yE}{B^2l^2} \end{align*} Thus the value of \(e/m\) is determined from the magnitudes of the electric and magnetic fields and the deflection \(y\).
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