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.

Answer 1

(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,

$r=\frac{mV}{qB}$,

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.