Solution Found!
Consider a particle of mass m, charge q, and constant
Chapter 31, Problem 85GP(choose chapter or problem)
Consider a particle of mass charge
, and constant speed
moving perpendicular to a uniform magnetic field of magnitude
, as shown in Figure
. The particle follows a circular path. Suppose the angular momentum of the particle about the center of its circular motion is quantized in the following way: \(\mathrm{mvr}=n \hbar\), where
\(n=1,2,3, \ldots\), and \(\hbar=h / 2 \pi\)
a. Show that the radii of its allowed orbits have the following values:
\(r_{n}=\sqrt{\frac{n \hbar}{q B}}\)
b. Find the speed of the particle in each allowed orbit.
Equation Transcription:
Text Transcription:
mvr=n \hbar
n=1,2,3, \ldots
\hbar=h / 2 \pi
r_n=\sqrt{\frac{n \hbar q B
Questions & Answers
QUESTION:
Consider a particle of mass charge
, and constant speed
moving perpendicular to a uniform magnetic field of magnitude
, as shown in Figure
. The particle follows a circular path. Suppose the angular momentum of the particle about the center of its circular motion is quantized in the following way: \(\mathrm{mvr}=n \hbar\), where
\(n=1,2,3, \ldots\), and \(\hbar=h / 2 \pi\)
a. Show that the radii of its allowed orbits have the following values:
\(r_{n}=\sqrt{\frac{n \hbar}{q B}}\)
b. Find the speed of the particle in each allowed orbit.
Equation Transcription:
Text Transcription:
mvr=n \hbar
n=1,2,3, \ldots
\hbar=h / 2 \pi
r_n=\sqrt{\frac{n \hbar q B
ANSWER:Step 1 of 3
The particle executes a circular motion just because its centripetal force is balanced with the magnetic force.
The centripetal force,
The magnetic force,
Where, 
