All Problems

Electric Current

Problem 3.210

A homogeneous proton beam accelerated by a potential difference \(V=600 \mathrm{kV}\) has a round cross-section of radius \(r\) \(=5.0 \mathrm{~mm} .\) Find the electric field strength on the surface of the beam and the potential difference between the surface and the axis of the beam if the beam current is equal to \(I=50 \mathrm{~mA}\).

Reveal Answer
E=(I/2πε0r)m/2eV=32 V/m,Δφ=(I/4πε0)m/2eV=0.8VE=\left(I / 2 \pi \varepsilon_{0} r\right) \sqrt{m / 2 e V}=32 \mathrm{~V} / \mathrm{m}, \Delta \varphi=\left(I / 4 \pi \varepsilon_{0}\right) \sqrt{m / 2 e V}=0.8V
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