Problem 24.25 describes two particles that orbit the earth's...

Name: Problem 26, Chapter 24: College Physics: A Strategic Approach
Uploaded: 2023-05-20T14:23:48-08:00
Duration: 2 min 57 s
Channel: Vishal Gupta
Description: Problem 24.25 describes two particles that orbit the earth's magnetic field lines. What is the frequency of the circular orbit for a. An electron with speed 1.0 ×10^6 m / s ? b. A proton with speed 5.0 ×10^4 m / s ?

Problem 24.25 describes two particles that orbit the earth's magnetic field lines. What is the frequency of the circular orbit for
a. An electron with speed $1.0 \times 10^{6} \mathrm{m} / \mathrm{s} ?$
b. A proton with speed $5.0 \times 10^{4} \mathrm{m} / \mathrm{s} ?$

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Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field. This force is perpendicular to both the direction of the particle’s velocity and the magnetic field, and it is the fundamental cause of the circular or helical trajectories that charged particles follow in a magnetic field.

Cyclotron Frequency

The cyclotron frequency is the frequency at which a charged particle orbits in a magnetic field. It is determined by the charge of the particle, the strength of the magnetic field, and the mass of the particle, and is given by the relation ? = |q|B/m for the angular frequency, or f = |q|B/(2?m) for the cyclic frequency.

Charge-to-Mass Ratio

The charge-to-mass ratio (q/m) of a particle is a critical parameter in determining its motion in a magnetic field. This ratio directly influences the cyclotron frequency, meaning particles with different charge-to-mass ratios will orbit at different frequencies even if they are moving in the same magnetic field.

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