# Electron Charge-to-Mass Ratio $\frac {e}{m}$

Based on the study of the electron movement in magnetic fields, the electron specific charge $\frac{e}{m}$ can be determined.
The balance of forces $F_{\text{Lorentz}}= F_{\text{Zentripetal}}$ can be determined as$$\frac{e}{m}=\frac{v_0}{r\cdot B}$$ Substitute $v_0$ by the here calculated term$${v_{\text{0}}=\sqrt{2\cdot \frac{e}{m}\cdot V_{\text a}}}$$ square and solve for $\frac {e}{m}$$\frac{e}{m}=\frac {2\cdot V_{\text a}}{r^2\cdot B^2}$$ Acceleration voltage$V_{\text a}$can be modified in the experiment, the magnetic field$B$can be calculated as shown here. It is proportional to the changeable coil current$I$. The radius$r$of the trajectory must be determined with the experiment. So you can get for example this table: So the experiment yields$\frac {e}{m}= (1.75\pm 0.06)\cdot 10^{11}\frac{\text C}{\text{kg}}$The literature value is$\bbox[5px,border:2px solid red]{\frac {e}{m}=1.75882\cdot 10^{11}\frac{\text C}{\text{kg}}}\$