The radius of the electron-trajectory in the magnetic field of Helmholtz coils

Because the electrons move on a circular trajectory the Lorentz force must be equal to the centripetal force:$$F_{\rm{Lorentz}}= F_{\rm{Zentripetal}}$$ Plug in the here deduced terms for the forces shows:$$e\cdot v_0 \cdot B = m_e\frac{{v_0}^2}{r}$$ Solved for r the radius of the electron-trajectory is$$\bbox[5px,border:2px solid red] {r = \frac {m_e\cdot v_0}{e\cdot B}}$$ This radius is known as Larmor radius or cyclotron radius. next