Question

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

Answer 1

Hint:Whenever a moving particle for ex: electron, proton, alpha particle enters in a magnetic field, the field exerts a force on these particles. If they enter perpendicular to field lines, due to the force they trace a circular path.

Complete step by step answer:
The force that magnetic field apply on moving charges is:
\[F = q\left( {v \times B} \right)\]
Force depends only on:-Velocity with which the particle enters the field, charge on the particle and the strength of the magnetic field.

As in question electrons and protons enter the field with the same velocity and magnetic field is also constant, the value of force depends on the charge held by the particle.As the charge on the electron is \[ - 1.602 \times {10^{ - 19}}\] and proton charge is \[1.602 \times {10^{ - 19}}\]. But we need to take only magnitude. Hence all the quantities used in the force formula are the same for both electron and proton.

Hence, the force exerted on the electron and proton by magnetic field will be equal.

Note:When the proton and electron will enter with different velocity then force will be greater for the particle whose velocity is greater. Though the mass of both particles varies but as the force exerted by the magnetic field is mass independent it is not taken into consideration.