Two point charges + Q and - Q having masses M and 2 M respectively, are projected from the same point with the same velocity v in the region of a uniform magnetic field B such that the velocity makes

Question

Two point charges + Q and - Q having masses M and 2 M respectively, are projected from the same point with the same velocity v in the region of a uniform magnetic field B such that the velocity makes an angle θ with the magnetic field. If we neglect the mutual interaction between the particles, the distance from the point of projection where they will meet again for the first time is

TestHub · Accepted Answer

Both the charged particle will follow the helical path and the particles will meet at the intersection of the two helix such that the pitch of one helix will be the integral multiple of the pitch of the other helix.

$T_{1} = \frac{2 π M}{QB}$

$T_{2} = \frac{2 π (2 M)}{QB}$

$T_{2} = \frac{4 π M}{QB}$

They will meet again when the first particle completes two revolutions and the second particle completes one revolution so distance will be given as

$d = v cos θ t = v cos θ . 2 \frac{(2 π M)}{QB} = \frac{4 π Mv cos θ}{QB}$

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