A certain particle is sent into a uniform magnetic field,...

Name: Problem 19, Chapter 28: Fundamentals of Physics
Uploaded: 2021-07-13T16:02:25-08:00
Duration: 3 min 6 s
Channel: Sheh Lit Chang

A certain particle is sent into a uniform magnetic field, with the particle's velocity vector perpendicular to the direction of the field. Figure $28-37$ gives the period $T$ of the particle's motion versus the inverse of the field magnitude $B .$ The vertical axis scale is set by $T_{s}=40.0 \mathrm{~ns}$, and the horizontal axis scale is set by $B_{s}^{-1}=5.0 \mathrm{~T}^{-1} .$ What is the ratio $m / q$ of the particle's mass to the magnitude of its charge?

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Key Concepts

Cyclotron Motion

When a charged particle enters a uniform magnetic field with its velocity perpendicular to the field, it undergoes circular motion due to the Lorentz force. The period of this circular motion is determined by the particle’s mass, charge, and the magnetic field strength. The fundamental relationship is given by T = 2?m/(qB), which is a cornerstone of cyclotron theory and has wide applications in areas such as mass spectrometry and particle accelerators.

Graphical Analysis of Proportional Relationships

Plotting the period (T) against the inverse of the magnetic field strength (1/B) yields a straight-line graph because T is directly proportional to 1/B in cyclotron motion. The slope of this linear graph is 2?m/q, and by determining the slope from the graph (using the given scaling factors), one can directly calculate the ratio m/q. This method of using graph interpretations to extract physical quantities is an important analytical tool in experimental physics.

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