Question

An electron travels with speed 9.0×106 m/s between the two parallel charged plates shown in the figure. The plates are separated by 1.0 cm and are charged by a 200 V battery. (Figure 1) What magnetic field strength will allow the electron to pass between the plates without being deflected?

Answer 1

The electric field strength is,

$$ \begin{aligned} E &=\frac{V}{d} \\ &=\frac{200}{1 \times 10^{-2}} \\ &=20000 \mathrm{~V} / \mathrm{m} \end{aligned} $$

Given that, the electron is not deflected between the plates.

So, the electro static force is balanced with the magnetic force. That is, \(q E=q v B\)

Hence, the magnetic field is, \(\begin{aligned} B &=\frac{E}{v} \\ &=\frac{20000}{\left(9.0 \times 10^{6}\right)} \\ &=2.2 \times 10^{-3} \mathrm{~T} \end{aligned}\)

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