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Question
Two ions have equal masses but one is singly-ionised and the other is doubly-ionised. They are projected from the same place in a uniform magnetic field with the same velocity perpendicular to the field.
(a) Both ions will move along circles of equal radii.
(b) The circle described by the singly-ionised charge will have a radius that is double that of the other circle.
(c) The two circles do not touch each other.
(d) The two circles touch each other.
Solution
(b) The circle described by the singly-ionised charge will have a radius that is double that of the other circle.
(d) The two circles touch each other.
The radius of the orbit of a charged particle in an external magnetic field,
`r = (mV)/(qB)`
where r is the radius of the circle, m is the mass of the ion, V is the velocity with which the ion is projected, q is the charge on the ion and B is the uniform magnetic field.
Since the mass m, the velocity V and the magnetic field B are same for both the ions, r is inversely proportional to the charge on the ion.
Hence, the radius of the circle described by the singly-charged ion will be twice the radius of the circle described by doubly-ionised ion.
Moreover, as both the charges are projected from the same place, the two circles described by them will touch each other at the point of projection.
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