Question

What is the direction of the magnetic force on the electron? What is the magnitude of magnetic force on an electron? What is the direction of the magnetic force on the proton? What is the magnitude of magnetic force on protons?

Answer 1

Hint: The magnetic force on any moving charged particle is given by the product of the charged particle and the vector product of velocity of the charged particle and the magnetic field. Using this formula, we shall determine the direction and magnitude of magnetic force on an electron and a proton.

Complete step-by-step solution:
Let us say there is a magnetic field ($\overrightarrow{B}$) perpendicular to the page coming outwards. And let us assume the electrons and protons are initially travelling with the same velocity as shown in the figure:

Here, we can see that they have the same velocity, are under the same magnetic field but their charges are equal and opposite.
The magnitude of magnetic force on electron and proton in this case will be same and equal to:
$\Rightarrow \left|F\right|=qvB$
Now, since they have opposite signs of charges, the direction of the net magnetic field on them will also be opposite. The direction of magnetic force on them can be calculated using Fleming’s right hand thumb rule and this direction is shown in the following diagram:

Here, we can see the direction of magnetic force on the proton is towards right and on electron is towards left.
Hence, the magnitude of force on electron and proton under the same conditions is equal but the direction of magnetic force is opposite due to opposite signs of these charges.

Note: In the above solution, we saw the direction and magnitude of force on an electron and proton, when they are initially under motion. If these particles are at rest in a magnetic field, then their velocity vector is zero, hence the net magnetic force acting on these particles will also be equal to zero.