An electricity and magnetism problem by Miraj Shah

Electricity and Magnetism Level 3

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 \(A\).


  • \(m\) deontes the mass of electron.

  • \(e\) denotes the magnitude of charge on an electron.


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