Question
Refer to the bubble chamber tracks in Fig. 19.15a. Suppose that particle 2 moves in a smaller circle than particle 1. Can we conclude that $\left|q_{2}\right|>\left|q_{1}\right|$ ? Explain.
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A bubble chamber is a device used in particle physics to visualize the paths of charged particles. When a charged particle moves through a magnetic field, it experiences a force perpendicular to its velocity and the magnetic field, causing it to move in a circular Show more…
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(II) Show that the angular momentum of the particle in Problem 21 is $L=q B r^{2}$ about the center of the circle.
Let us sketch the diagram for the motion of the particle of mass $m$ along the circle of radius $R$ and indicate $x$ and $y$ axis, as shown in the figure. (a) For the particle, change in momentum $\Delta \vec{p}=m v(-\vec{i})-m v(\vec{j})$ so, $|\Delta \vec{p}|=\sqrt{2} m v$ and time taken in describing quarter of the circle, Hence, $\langle\vec{F}\rangle=\frac{|\Delta \vec{p}|}{\Delta t}=\frac{\sqrt{2} m v}{\pi R / 2 v}=\frac{2 \sqrt{2} m v^{2}}{\pi R}$ (b) In this case $\overrightarrow{p_{i}}=0$ and $\overrightarrow{p_{f}}=m w_{t} t(-\vec{i})$ so $|\Delta \vec{p}|=m w_{t} t$ Hence, $|<\vec{F}\rangle \mid=\frac{|\Delta \vec{p}|}{t}=m w_{t}$
Physical Fundamentals Of Mdchanics
The Fundamental Equation of Dynamics
If $m, p$ and $l$ denote respectively the mass, lincar momentum and angular momentum of a particle moving on a circle of radius $r$, then the kinetic energ of the particle can be cxpressed as (a) $\frac{p^{2}}{2 m}$ (b) $\frac{l^{2}}{2 m}$ (c) $\frac{p^{2}}{2 m r^{2}}$ (d) $\frac{l^{2}}{2 m r^{2}}$
Work, Energy, Power and Circular Motion
Section B
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