Subject: Physics
The ratio of charge to mass is called the specific charge.
Principle: If a beam of electrons is subjected to electric and magnetic fields it experiences forces. By adjusting the magnitude and direction of the two fields, the net force on the electron is made zero.
The apparatus consists of a cathode C and anode A which are enclosed in an evacuated discharge tube. When a high potential difference is applied between cathode and anode, a narrow beam of cathode rays emerges from a small hole in the anode and passes between two parallel plates P1 and P2. A uniform electric field is applied to the plane of paper with the help of horizontal plates P1 and P2 and the electrons will deflect upwards (i.e. towards point S2) in the plane of the paper. On the other hand, a uniform magnetic field is also applied in this region perpendicular to the plane of the paper and inward direction. The magnetic field will deflect the electrons downwards (towards point S1) in the plane of the paper.
If the uniform magnetic field is applied, then force on electron on electron due to the magnetic field, Fm = Bev, where e is the changes on an electron, B is the magnetic field strength and v is the velocity of the electron.
The force Be v is always normal to the path of electron beam and therefore moves the electron along circular path. Hence, the force on electron due to magnetic field provides necessary centripetal force and therefore,
\begin{align*} Bev &= \frac {mv^2}{r} \\ \text {or,} \: \frac em &= \frac {v}{rB} \\ \end{align*}
Therefore, to find \( \frac em \) , we have to determine B, v and r.
Now, from the right angled DQSS1
\begin{align*} \tan \theta &= \frac {SS_1}{QS} = \frac yL \\ \text {Since} \: \theta \text {is small} \\ \therefore \tan \theta \approx \theta \\ \therefore \theta &= \frac yL \dots (i) \\ \text {OA is an arc whose length is nearly equal to l,} \\ \therefore \theta = \frac {\widehat {OA}}{OC} = \frac {\text {arc length}}{\text {radius}} \\ \text {or,} \: \theta &= \frac lr \dots (ii) \\ \text {Therefore, from equation} \: (i) \text {and} \: (ii), \text {we have} \\ \frac lr &= \frac yL \\ \text {or,} \: r &= \frac {l \times L}{y} \dots (iii) \\ \end{align*}
From the experimental arrangement the value of l, L and y can be measured. Thus, from the relation value of r can be calculated.
Knowing the values of B, v and r, the value of e/m of an electron can be calculated which equal to 1.77 × 1011 C kg-1.
Reference
Manu Kumar Khatry, Manoj Kumar Thapa, et al. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.
S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.
The ratio of charge to mass is called the specific charge.
If a beam of electrons is subjected to electric and magnetic fields it experiences forces.
If the uniform magnetic field is applied, then force on electron on electron due to the magnetic field, Fm = Bev, where e is the changes on an electron, B is the magnetic field strength and v is the velocity of the electron.
The force Be v is always normal to the path of an electron beam and, therefore, moves the electron along a circular path.
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