A beam of electrons whose kinetic energy is K emerges from a thin-foil “window” at the end of an accelerator tube. There is a metal plate a distance d from this window and at right angles to the direction of the emerging beam. (a) We have to show that we can prevent the beam from hitting the plate if we apply a magnetic field B such that

In which m and e are the electron mass and charge. (b) We have to identify the orientation of .

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Let the kinetic energy of the electron beam as it emerges out of the accelerator tube be K. Let the speed of the electrons having kinetic energy K be v. We have

Let the magnetic field be uniform and be perpendicular to the direction of the velocity of the electron beam. As the electrons are negatively charged and force on the electrons in magnetic field is given by

If we want the electron beam to move in counter-clockwise direction, as shown in the figure, direction of the magnetic field vector has to be perpendicular to the plane of the figure emerging out of it.

In a uniform magnetic field the magnitude of the velocity of electrons remains constant and only the direction of their velocity changes. Electrons will move in a circular orbit. If we have to adjust the magnitude of the magnetic field such that the electron beam just grazes along the metal sheet, which is at a distance d from the exit of the accelerator tube, the radius of their circular orbit has to be just equal to d. We have

If we want to prevent the electron beam to touch the metal plate,