
The radius of curvature of the path of the charged particle in a uniform magnetic field is directly proportional to
A. The charge on the particle
B. The momentum of the particle
C. The energy of the particle
D. The intensity of the field
Answer
161.1k+ views
Hint:A magnetic field is the area around a magnet or moving charges where its force can be felt. The force due to a magnetic field will be calculated by Lorentz force. The expression of radius of the curvature is obtained by equating the Lorentz force and centripetal force.
Formula used:
The radius of the circular path will be mathematically written by the following formula:
\[r = \dfrac{{mv}}{{qB}}\] ……(i)
Where ‘m’ is the mass of the charge, ‘v’ is the velocity with which it is moving and ‘B’ is the magnetic field.
Complete step by step solution:
The force experienced by a charge due to a magnetic field can cause a charge to move in a spiral or circular path. This radius of the circular path will be mathematically written by the following formula:
\[r = \dfrac{{mv}}{{qB}}\] ……(i)
Also, since the charge is in motion, it will also have some momentum. The momentum of the charged particle is given as the product of mass of the particle and its velocity. It is represented by the letter ‘p’. Mathematically, it is written as,
p=mv
Therefore, equation (i) can be written as,
\[r = \dfrac{p}{{qB}}\]
Since the charge and magnetic field are constant, therefore the above equation can also be written as,
\[r \propto p\]
The radius of curvature of the path of the charged particle in a uniform magnetic field is directly proportional to the momentum of the particle.
Hence, option B is the correct answer.
Note: Since, the current will be passing through the conductor, an electric field will be produced. Also, since the conductor will start behaving as a magnet, the magnetic field will also be there. These electric and magnetic effects will create a force together also known as the Lorentz force which was first observed by Hendrik Antoon Lorentz in 1895.
Formula used:
The radius of the circular path will be mathematically written by the following formula:
\[r = \dfrac{{mv}}{{qB}}\] ……(i)
Where ‘m’ is the mass of the charge, ‘v’ is the velocity with which it is moving and ‘B’ is the magnetic field.
Complete step by step solution:
The force experienced by a charge due to a magnetic field can cause a charge to move in a spiral or circular path. This radius of the circular path will be mathematically written by the following formula:
\[r = \dfrac{{mv}}{{qB}}\] ……(i)
Also, since the charge is in motion, it will also have some momentum. The momentum of the charged particle is given as the product of mass of the particle and its velocity. It is represented by the letter ‘p’. Mathematically, it is written as,
p=mv
Therefore, equation (i) can be written as,
\[r = \dfrac{p}{{qB}}\]
Since the charge and magnetic field are constant, therefore the above equation can also be written as,
\[r \propto p\]
The radius of curvature of the path of the charged particle in a uniform magnetic field is directly proportional to the momentum of the particle.
Hence, option B is the correct answer.
Note: Since, the current will be passing through the conductor, an electric field will be produced. Also, since the conductor will start behaving as a magnet, the magnetic field will also be there. These electric and magnetic effects will create a force together also known as the Lorentz force which was first observed by Hendrik Antoon Lorentz in 1895.
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
