JEE Exam > JEE Questions > A proton, an electron, and a Helium nucleus, ...
Start Learning for Free
A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,?
Most Upvoted Answer
A proton, an electron, and a Helium nucleus, have the same energy. The...
Introduction:
In this scenario, a proton, an electron, and a Helium nucleus are in circular orbits in a plane due to a perpendicular magnetic field. We need to determine the radii of their respective orbits.
Explanation:
To analyze the situation, we can use the following principles:
1. The magnetic force on a charged particle moving in a magnetic field is given by the equation F = qvBsinθ, where F is the magnetic force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field, and θ is the angle between the velocity and the magnetic field.
2. The centripetal force required to keep a particle in circular motion is given by the equation F = mv²/r, where m is the mass of the particle, v is the velocity of the particle, and r is the radius of the circular orbit.
Proton:
Given that the proton, electron, and Helium nucleus have the same energy, they will have the same velocity. Let's denote this velocity as v.
The magnetic force on the proton is F = qvBsinθ. Since the velocity and magnetic field are perpendicular, sinθ = 1, and the force becomes F = qvB.
The centripetal force required to keep the proton in a circular orbit is F = mv²/r.
Equating the two forces, we have qvB = mv²/r. Rearranging the equation, we get r = mv/qB.
Electron:
Using the same principles, the magnetic force on the electron is F = qvBsinθ. Since the velocity and magnetic field are perpendicular, sinθ = 1, and the force becomes F = qvB.
The centripetal force required to keep the electron in a circular orbit is F = mv²/r.
Equating the two forces, we have qvB = mv²/r. Rearranging the equation, we get r = mv/qB.
Helium Nucleus:
The Helium nucleus consists of two protons and two neutrons, but since the question states that the Helium nucleus has the same energy as the proton and electron, we can consider it as a single particle with double the charge of a proton.
Using the same principles, the magnetic force on the Helium nucleus is F = 2qvBsinθ. Since the velocity and magnetic field are perpendicular, sinθ = 1, and the force becomes F = 2qvB.
The centripetal force required to keep the Helium nucleus in a circular orbit is F = mv²/r.
Equating the two forces, we have 2qvB = mv²/r. Rearranging the equation, we get r = 2mv/qB.
Conclusion:
In summary, the radii of the circular orbits for the proton, electron, and Helium nucleus are given by r = mv/qB, r = mv/qB, and r = 2mv/qB, respectively.
In this scenario, a proton, an electron, and a Helium nucleus are in circular orbits in a plane due to a perpendicular magnetic field. We need to determine the radii of their respective orbits.
Explanation:
To analyze the situation, we can use the following principles:
1. The magnetic force on a charged particle moving in a magnetic field is given by the equation F = qvBsinθ, where F is the magnetic force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field, and θ is the angle between the velocity and the magnetic field.
2. The centripetal force required to keep a particle in circular motion is given by the equation F = mv²/r, where m is the mass of the particle, v is the velocity of the particle, and r is the radius of the circular orbit.
Proton:
Given that the proton, electron, and Helium nucleus have the same energy, they will have the same velocity. Let's denote this velocity as v.
The magnetic force on the proton is F = qvBsinθ. Since the velocity and magnetic field are perpendicular, sinθ = 1, and the force becomes F = qvB.
The centripetal force required to keep the proton in a circular orbit is F = mv²/r.
Equating the two forces, we have qvB = mv²/r. Rearranging the equation, we get r = mv/qB.
Electron:
Using the same principles, the magnetic force on the electron is F = qvBsinθ. Since the velocity and magnetic field are perpendicular, sinθ = 1, and the force becomes F = qvB.
The centripetal force required to keep the electron in a circular orbit is F = mv²/r.
Equating the two forces, we have qvB = mv²/r. Rearranging the equation, we get r = mv/qB.
Helium Nucleus:
The Helium nucleus consists of two protons and two neutrons, but since the question states that the Helium nucleus has the same energy as the proton and electron, we can consider it as a single particle with double the charge of a proton.
Using the same principles, the magnetic force on the Helium nucleus is F = 2qvBsinθ. Since the velocity and magnetic field are perpendicular, sinθ = 1, and the force becomes F = 2qvB.
The centripetal force required to keep the Helium nucleus in a circular orbit is F = mv²/r.
Equating the two forces, we have 2qvB = mv²/r. Rearranging the equation, we get r = 2mv/qB.
Conclusion:
In summary, the radii of the circular orbits for the proton, electron, and Helium nucleus are given by r = mv/qB, r = mv/qB, and r = 2mv/qB, respectively.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,?
Question Description
A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,?.
A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,?.
Solutions for A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? defined & explained in the simplest way possible. Besides giving the explanation of
A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,?, a detailed solution for A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? has been provided alongside types of A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? theory, EduRev gives you an
ample number of questions to practice A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r. r. and He be their respective radii, then,? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup