A magnetic field is non-uniform along the z axis between z = 0 and z = L, with t

Question

A magnetic field is non-uniform along the z axis between z = 0 and z = L, with the components (-B_r, 0, B_z) expressed in cylindrical coordinates (r, phi, z), and uniform everywhere else: B = B_z. An electron and a proton, initially in cyclotron motion around B_z at z = 0 with the centers of their orbits at r = 0, are moved to z = L/2 without interrupting their circular motion. Which of the following describes correctly the subsequent motions of these particles? While gyrating around B_z, both particles move to z = L. While gyrating around B_z, both particles move back to z = 0. Particles now gyrate both around B_z and B_r at z = L/2 The electron moves to z = 0 and the proton to z = L.

Explanation / Answer

According to the question

We know that

The subsequent motions of these particles is

while grating around Bz

both particles move back to Z=0

So option B) is correct

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