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In the given arrangement, the space between
a pair of co-axial cylindrical conductors is
evacuated. The outer cylinder, called anode,
may be given a positive potential \( V \) relative
to the inner cylinder.
A static homogeneous magnetic field \( \vec{B} \)
parallel to the cylinder axis, directed out of
plane of figure is also present. Induced charges in the conductors
are neglected.
We study the dynamics of electrons with rest mass \( m \) and
charge \( e \). The electrons are released at the surface of inner
cylinder. Consider the following two cases:
Case 1: Firstly the potential \( V \) is turned on, but \( \vec{B}=0 \). An
electron with negligible velocity is ejected at the surface of inner
cylinder. It is found to hit the anode.
Case 2: Now \( V=0 \) but \( \vec{B} \) is present. An electron starts out with
an initial velocity \( \vec{v}_{0} \) in radial direction. For magnetic field larger
than critical value \( B_{c} \) the electron will not reach the anode.
\( \begin{array}{ll}\text { Considering case } 2 \text {, the trajectory of electron will be } \\ \text { (1) Straight line } & \text { (2) Circular } \\ \text { (3) Parabolic } & \text { (4) Helical }\end{array} \)
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