Question

An electron and proton enter a magnetic field with equal velocities. Which one of them experiences a greater force?

Answer 1

Lorentz force

1. We know if a charge $q$ is moving with a velocity $v$ in a magnetic field, then the Lorentz force exerted on the charge is given by the form, $\overrightarrow{F}=q\left(\overrightarrow{V}\times \overrightarrow{B}\right)$
2. We know from the vector algebra that, the cross product of two vectors is always directed perpendicular to the plane made by the two vectors. The magnetic force will be zero when v and B are in the same direction.

The magnetic force exerted on the proton and electron

1. We know, the charge of electron and proton is equal but opposite. According to the question, the proton and electron are moving with the same velocity in the same magnetic field.
2. From the formulae of Lorentz force, we know that magnetic force exerted on a charged particle is $\overrightarrow{F}=q\left(\overrightarrow{V}\times \overrightarrow{B}\right)$. In this case velocity of electron and proton is the same and the magnetic field is constant in this case.
3. So, the force exerted on the electron and proton is equal but their directions are opposite because the electron and proton are the opposite charges.

Hence, the magnetic force exerted on the electron and proton due to the magnetic field will be equal but the directions will be opposite.