Physics Asked by Rahul Maurya on July 17, 2021
So here is the condition. There are 3 charged particles, all three of them have the same charge, but they have different masses and all of them are moving with the same velocity. In a magnetic field, will they experience the same force?
My teacher said that they would experience different forces because they have different masses, I was quite skeptical as F = q (V vector X B vector), so posted the same question here.
The force acting to the particle in electromagnetic field is $$mathbf{F} = qmathbf{E} + qmathbf{v}timesmathbf{B},$$ which is independent on mass. Thus, the force on all the three particles will be the same. However, mass enters the Newton's second law $$mmathbf{a}=mathbf{F},$$ which means that the three particles will experience different acceleration and consequently they will have different trajectories.
Correct answer by Roger Vadim on July 17, 2021
Yes, they all experience the same force. The Lorentz-force is proportional to the speed and charge of a particle as well as the strength of the magnetic field.
The acceleration of the particles however is equal to the force that acts upon them divided by their respective mass. Hence, it differs for the three particles. Therefore, they will not move on the same trajectories (but for e.g. a homogeneous field on circles with different radii).
Answered by Herr_Mitesch on July 17, 2021
Assuming that you mean a homogenous field and that we're ignoring the force they exert on each other, yes, they will experience the same force - at first, that is. The same force has different effects on different masses. They will all move in circles or spirals, since Lorentz force is always perpendicular to their velocity and the magnetic field. They will also have the same speed on this trajectory. But the radii of the spirals will depend on their mass, and so their velocities will have different directions. Since the direction of the Lorentz force depends on the direction of travel, the forces will be different as soon as their trajectories diverge. Which they will, unless they are moving parallel to the magnetic field.
Answered by Vercassivelaunos on July 17, 2021
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