Question

Which of the following particles will describe the smallest circle when projected with the same velocity perpendicular to a magnetic field?

Options

• Electron

•  Proton

• He⁺

•  Li⁺

Answer 1

Electron 

When a particle moves in a magnetic field, the necessary centripetal force, for  the particle to move in a circle, is provided by the magnetic force acting on the particle.
So, equating the Lorentz force with the cetripetal force for a charged particle of charge q describing a circle of radius r, we get:
`qvB = (mv^2)/r`

`⇒ r = "(mv)"/"qB"`

Here, m is the mass of the particle and v is its velocity.
The amount of charge of all the given particles is same; hence, for a given charge, r ∝ m . And since the electron is the lightest of all the particles, it describes the smallest circle when projected with the same velocity perpendicular to the magnetic field.