All Problems

Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.385

From the surface of a round wire of radius \(a\) carrying a direct current \(I\) an electron escapes with a velocity \(v_{0}\) perpendicular to the surface. Find what will be the maximum distance of the electron from the axis of the wire before it turns back due to the action of the magnetic field generated by the current.

Reveal Answer
rmax=aev0/b, where b=μ02πemIr_{m a x}=a \mathrm{e}^{v_{0} / b}, \quad \text { where } \quad b=\frac{\mu_{0}}{2 \pi} \frac{e}{m} I
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