Particle in a uniform magnetic field

In summary, a particle in a uniform magnetic field refers to the motion of a charged particle in a constant magnetic field, which results in a circular or helical path. This motion is influenced by the strength of the magnetic field, particle's charge and mass, and its velocity. The force on the particle can be calculated using the equation F = qvB, where q is the charge, v is the velocity, and B is the magnetic field strength. The trajectory of the particle depends on its initial conditions, with a perpendicular velocity resulting in a circular path and a parallel velocity resulting in a helical path. This concept has various real-world applications, including in particle accelerators, mass spectrometers, and MRI machines, and helps us
  • #1
bowdish.9
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Homework Statement


A particle with charge q and kinetic energy K travels in a uniform magnetic field of magnitude B. If the particle moves in a circular path of radius R, find expressions for speed, v, and mass, m.. (Use any variable or symbol stated above as necessary.)

Homework Equations


K=1/2mv^2 F=qvB=(mv^2)/R

The Attempt at a Solution


2K=mv^2 ---> qvB=(2K)/R ---> (2K)/(qBR)

Why is this incorrect?
 
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  • #2
If this is supposed to be the velocity, it looks correct (if we do not include special relativity).
Why do you think it is incorrect?
 

Related to Particle in a uniform magnetic field

1. What is a particle in a uniform magnetic field?

A particle in a uniform magnetic field is a type of motion that occurs when a charged particle is moving in a constant magnetic field. The particle experiences a force due to the magnetic field, causing it to move in a circular or helical path.

2. What factors influence the motion of a particle in a uniform magnetic field?

The motion of a particle in a uniform magnetic field is influenced by the strength of the magnetic field, the charge and mass of the particle, and the velocity of the particle. These factors determine the magnitude and direction of the force acting on the particle.

3. What is the equation for the force on a particle in a uniform magnetic field?

The force on a particle in a uniform magnetic field can be calculated using the equation F = qvB, where q is the charge of the particle, v is its velocity, and B is the magnetic field strength. The direction of the force is perpendicular to both the velocity and the magnetic field.

4. How does the trajectory of a particle in a uniform magnetic field change with different initial conditions?

The trajectory of a particle in a uniform magnetic field depends on its initial velocity and direction. If the initial velocity is perpendicular to the magnetic field, the particle will move in a circular path. If the initial velocity has a component parallel to the magnetic field, the particle will move in a helical path.

5. What is the significance of particle in a uniform magnetic field in real-world applications?

Particle in a uniform magnetic field has many practical applications, such as in particle accelerators, mass spectrometers, and magnetic resonance imaging (MRI) machines. It also helps us understand the behavior of charged particles in space, such as the Van Allen radiation belts.

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