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 go along circles of equal radii
• B. The circle described by the single-ionised charge will have a radius double that of the other circle.
• C. The two circles do not touch each other
• D. The two circle touch each other

Answer 1

Answer: (B), (D)

The correct options are
B The circle described by the single-ionised charge will have a radius double that of the other circle.
D The two circle touch each other

The radius $r$ of the path of charged particle with charge q in a uniform magnetic field(B) is given by
$r=\frac{mv}{qB}$
where, $m$ is mass of the particle.
Now, if charge of singly ionized ion is $e$, then charge of doubly ionized ion is $2e$. Hence, the circle described by the singly ionized charge will have a radius double that of the other one. The two circle will touch each other because ions are projected from the same place.