From an electron gun, electrons are emitted with negligible speed and subsequently accelerated along the x -axis by a potential difference V . Emerging from a narrow hole, these electrons enter a uniform magnetic field B that points along the same axis. A fraction of the electrons exiting the hole do so at slightly divergent angles, as shown in the figure. Determine the distance along the x -axis at which these parax

Step-by-step solution

The kinetic energy of the electron after being accelerated by a potential difference V is given by: 1 2 mv^2 = eV v = 2eV m The electrons enter the magnetic field at a small angle (since they are paraxial) with the x -axis. The velocity component parallel to the magnetic field is: v_ = v v The time period of one revolution in the uniform magnetic field is independent of the velocity and is given by: T = 2 m eB The electrons will refocus on the x -axis after completing one full revolution. The distance along the x -