# An electricity and magnetism problem by Miraj Shah

Electrons are ejected from the electron gun with negligible velocity. These emitted electrons are then accelerated across a potential difference $$V$$ along the $$x$$-axis. These electrons emerge from a narrow hole into a region of uniform magnetic field $$B$$. However, some of the electrons emerging from the hole make slightly divergent angles as shown in the figure above. If the paraxial electrons are refocused on the $$x$$-axis. at a distance $$\sqrt{\dfrac{A \pi^2 mV}{eB^2}}$$ from the hole, then find the value of $$A$$.

Notations:

• $$m$$ deontes the mass of electron.

• $$e$$ denotes the magnitude of charge on an electron.

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