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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.
The critical magnetic field \( B_{C} \) is given by
(1) \( \frac{2 m v_{0}}{e b} \)
(2) \( \frac{m v_{0}}{e b} \)
(3) \( \frac{2 b m v_{0}}{e\left(b^{2}-a^{2}\right)} \)
(4) \( \frac{2 a m v_{0}}{e\left(b^{2}-a^{2}\right)} \)
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