Calculate the cyclotron frequency of a proton in a magnetic field of magnitude 5.20 T .

Name: Problem 35, Chapter 29: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2021-01-02T03:51:48-08:00
Duration: 2 min 41 s
Channel: Laszlo Zalavari
Description: Calculate the cyclotron frequency of a proton in a magnetic field of magnitude 5.20 T .

Calculate the cyclotron frequency of a proton in a magnetic...

Key Concepts

Cyclotron Frequency

Cyclotron frequency is the rate at which a charged particle orbits in a uniform magnetic field. It is determined by the particle’s charge and mass, and the strength of the magnetic field. The key formula, f = (qB)/(2?m), shows that this frequency is independent of the particle’s speed or the radius of the orbit, making it a fundamental concept in classical electromagnetism and accelerator physics.

Lorentz Force

The Lorentz force is the force exerted on a moving charged particle in electromagnetic fields, and is given by F = q(v × B). In the context of cyclotron motion, this force acts perpendicular to the velocity of the particle, causing it to follow a circular path in a magnetic field. Understanding the Lorentz force is essential for deriving the equations of motion in magnetic fields.

Charge-to-Mass Ratio

The charge-to-mass ratio (q/m) is a critical parameter in determining the behavior of charged particles in magnetic fields. It appears directly in the cyclotron frequency formula and influences how strongly a particle will respond to the magnetic field. This ratio is fundamental in various applications, from mass spectrometry to the design of particle accelerators.

Magnetic Field

The magnetic field is a vector field that exerts forces on moving charges and magnetic dipoles. In the context of charged particle motion, its magnitude and direction are crucial in determining the curvature of the particle's path. A stronger magnetic field results in a higher cyclotron frequency, which is a key aspect of controlling charged particle beams in devices like cyclotrons.

Transcript

0:00 Hello everyone.

00:01 In this problem, we're asked to find the angular frequency or the cyclotron frequency of a proton that is moving around in a cyclotron.

00:10 Essentially, what's happening here is that you have a uniform magnetic field b perpendicular to which the proton is moving in a circle.

00:19 And so the proton has a mass of 1 .67 times 10 to minus 27 kilograms.

00:23 The field strength we are given is equal to 5 .20 teslas.

00:29 And we know that the charge of the proton is 1 .60 times 10 minus 19 kuloms.

00:35 So what's happening here is that we have the force acting on the proton is the lawrence force, even by q times v times b, provided that the proton is metering perpendicularly to the demand any field, which i have assumed over here.

00:50 And this is equal to the mass times the eight.

00:53 Acceleration, so the newtonian force that's acting on the proton responsible for the motion.

00:59 But now, since the proton is moving in a circle, we also know that the acceleration is that of the centripetal acceleration, which is v squared divided by r.

01:09 For amorven, no doubt at b is equal to two pi times the radius of the motion, of the circular motion, divided by the period of the motion.

01:19 And so this is just saying that, you know, the proton moves around one circumference, covers a length of one circumference in one period.

01:29 And so 1 over t is just equal to f...

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