Question

If a proton is projected in a direction perpendicular to a uniform magnetic field with velocity \[v\] and an electron is projected along the magnetic field, what will happen to proton and electron?
A. The electron will travel along a circle with constant speed and also the proton will move along a straight line.
B. A proton will move in a circular path with constant speed and there will be no effect on the motion of the electron.
C. There will not be any side effects on the motion of the electron and proton.
D. The electron and proton both will follow the path of a parabola.

Answer 1

Hint: In the given question, we need to find the condition of the proton and electron. For this, we need to use the formula for force experienced by a charged particle in an external magnetic field to get the desired result.





Formula used:
The following formula is used for solving the given question.
The magnetic force on moving charge is given by
 \[\vec F = q(\vec v \times \vec B) = qvBsin\theta \]
Here, \[F\] is the force, \[v\] is the velocity, \[B\] is the magnetic field strength, and \[q\] is charge.


Complete answer:
We know that the magnetic force on the moving charge is \[\vec F = q(\vec v \times \vec B) = qvBsin\theta \]
Here, \[F\]is the force, \[v\] is the velocity, \[B\] is the magnetic field strength, and \[q\] is charge.
So, for Proton, we can say that \[\theta = {90^ \circ }\]
Also, for electron, \[\theta = {0^ \circ }\]
Therefore, maximum force will act on the proton in a direction perpendicular to both \[\vec v\] and \[\vec B\], so it will move along a circular path.
Thus, we can say that force on an electron will be zero because it is moving parallel to the field.
Therefore, the correct option is (B).


Note: Many students make mistakes in writing the formula of the magnetic force on the moving charge. This is the only way through which we can solve the example in the simplest way. Also, it is essential to analyze the formula carefully to get the desired result regarding proton and electron.