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 aslo 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.
Considering case 2, the trajectory of electron will be

Options

A. straight line
B. Circular
C. Parabolic
D. Helical

Answer

B

Explanation

When `V=0`, the electron moves in homogenous static field B. The magnetic field acts orthogonal to the velocity and hence electron moves in a circle.
Hence choice (b) is correct.