A particle undergoes uniform circular motion of radius 26.1 μm in a uniform magnetic field. The

Name: Problem 28, Chapter 28: Fundamentals of Physics
Uploaded: 2019-07-24T04:14:44-08:00
Duration: 1 min 51 s
Channel: Shital Rijal
Description: A particle undergoes uniform circular motion of radius 26.1 μm in a uniform magnetic field. The magnetic force on the particle has a magnitude of 1.60 ×10^-17 N. What is the kinetic energy of the particle?

step 1 So the question says that a particle undergoes an informed circle motion of radius are equals to

Question

A particle undergoes uniform circular motion of radius $26.1 \mu \mathrm{m}$ in a uniform magnetic field. The magnetic force on the particle has a magnitude of $1.60 \times 10^{-17} \mathrm{~N}$. What is the kinetic energy of the particle?

   A particle undergoes uniform circular motion of radius $26.1 \mu \mathrm{m}$ in a uniform magnetic field. The magnetic force on the particle has a magnitude of $1.60 \times 10^{-17} \mathrm{~N}$. What is the kinetic energy of the particle?

Fundamentals of Physics

David Halliday,… 10th Edition

Chapter 28, Problem 28

Instant Answer

Solved by Expert Shital Rijal

07/24/2019

Step 1

We know that the magnetic force on the particle is given by the equation F = qvB, where F is the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnetic field strength. Show more…

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A particle undergoes uniform circular motion of radius $26.1 \mu \mathrm{m}$ in a uniform magnetic field. The magnetic force on the particle has a magnitude of $1.60 \times 10^{-17} \mathrm{~N}$. What is the kinetic energy of the particle?

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Key Concepts

Cyclotron Motion and Period

The period of the circular motion of a charged particle in a magnetic field is determined by the cyclotron frequency, which is given by ? = qB/m. The corresponding period, T = 2?m/(qB), shows that the motion's period is directly proportional to the mass-to-charge ratio (m/q) and inversely proportional to the magnetic field strength. This relationship is key in understanding the dynamics of charged particles in magnetic fields, as seen in devices like cyclotrons.

Magnetic Force on Charged Particles

In a uniform magnetic field, a charged particle experiences a one-to-one force given by the Lorentz force, which acts perpendicular to both the magnetic field and the velocity of the particle. This causes the particle to undergo circular motion, with the magnetic force providing the necessary centripetal force to sustain the circular path.

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