
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
161.7k+ views
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.
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.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

Young's Double Slit Experiment Step by Step Derivation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Displacement-Time Graph and Velocity-Time Graph for JEE

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

Uniform Acceleration

Degree of Dissociation and Its Formula With Solved Example for JEE
