Question

A proton and an electron both moving with the same velocity v enter into a region of magnetic field directed perpendicular to the velocity of the particles. They will now move in circular orbits such that
A. Their time periods will be the same.
B. Their time period for protons will be higher.
C. Their time period for electrons will be higher.
D. Their orbital radii will be the same.

Answer 1

Hint: In the given question, we need to determine how protons and electrons will move in a circular orbit. For this, we have to use the following formula to get the desired result.

Formula used:
The following formulae are used to solve the given question.
The time period of a particle moving along a circular path is \[T = \dfrac{{2\pi m}}{{qB}}\].
Here, \[T\] is the time, \[m\] is the mass , \[q\] is the charge , and \[B\] is the magnetic field of intensity.


Complete answer:
We know that the time period of particle moving along a circular path is \[T = \dfrac{{2\pi m}}{{qB}}\]
Here, \[T\]is the time, \[m\] is the mass , \[q\] is the charge , and \[B\] is the magnetic field of intensity.
This indicates that there is a direct relationship between \[T\] and \[m\].
Mathematically, it is given by
 \[T\alpha m\]
But \[q\] and \[B\] are the same.
Thus, we can say that the mass of protons is greater than the mass of electrons.
Hence, the time period of a proton is greater than the time period of an electron.

Therefore, the correct option is (B).




Note:Many students make mistakes in analyzing the formula of time period of a particle moving along a circular path. That means, it is necessary to understand the relationship between the parameters such as \[q,B,m,\] and \[T\] to get the desired result.