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(Problem 10, Chapter 2, Modern Physics - Serway)

1. The problem statement, all variables and given/known data

Recall that the magnetic force on a charge q moving with velocity [tex]\vec{v}[/tex] in a magnetic field [tex]\vec{B}[/tex] is equal to [tex]q\vec{v}\times\vec{B}[/tex]. If a charged particle moves in a circular orbit with a fixed speed [tex]v[/tex] in the presence of a constant magnetic field, use the relativistic form of Newton's second law to show that the frequency of its orbital motion is

[tex]

f=\frac{qB}{2\pi m}(1-\frac{v^2}{c^2})^{1/2}

[/tex]

2. Relevant equations

[tex]

F=\frac{ma}{(1-v^2/c^2)^{3/2}}

[/tex]

3. The attempt at a solution

The particle moves in a circle then the magnetic field is perpendicular to the velocity and [tex]F=qvB[/tex].

[tex]

f=\frac{v}{2\pi R}

[/tex]

[tex]

qvB=\frac{ma}{(1-v^2/c^2)^{3/2}}

=\frac{m}{(1-v^2/c^2)^{3/2}}\frac{v^2}{R}

[/tex]

[tex]

R=\frac{mv}{(1-v^2/c^2)^{3/2}qB}

[/tex]

[tex]

f=\frac{(1-v^2/c^2)^{3/2}qB}{2\pi m}

[/tex]

What's wrong?

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# Homework Help: Relativistic form of Newton's second law

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