Question

Two ions have equal masses but one is singly- ionized and the other is doubly- ionized. They are pojected from the same place in a uniform magnetic field with the same velocity perpendicular to the field.
A. the two circles touch each other
B. the two circles do not touch each other
C. the circle described by the singly-ionized charge will have a radius double that of the other circle
D. both the ions will go along circles of equal radii.

Answer 1

Correct Answer - A::C
When a charged particle is subjected to a perpendicular magnetic field, it will describe a circular path of radius, `r=mv//Bq` i.e. `rprop1//(q//m)`. Thus option (c) is true. As time period of revolution, `T=(2pim)/(Bq)` is independent of v and r, so the particle will return to its initial position after one revolution, hence the two particles of different charges will return to their initial positions after one revolution and their paths will touch each other there.