(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A charged particle (mass [itex]m[/itex], charge [itex]q[/itex]) is moving with constant speed [itex]v[/itex]. A magnetic field [itex]\vec{B}[/itex] is perpendicular to the velocity of the particle. Find the strength of the field required to hold the particle on a circular orbit of radius [itex]R[/itex].

2. Relevant equations

[itex]\vec{F} = q\vec{v} \times \vec{B}[/itex]

[itex]\vec{F} = m\vec{a}_c[/itex]

3. The attempt at a solution

Well, I know that in the "classical" case this is fairly easy. One just sets

[itex]qvB = ma[/itex],

and since [itex]a = \frac{v^2}{R}[/itex], one gets

[itex]qvB = m \frac{v^2}{R}[/itex]

[itex] \Rightarrow B = \frac{mv}{qR}[/itex]

However, I am not sure if I can use this here, because the particle is assumed to be travelling at close to the speed of light. I have read somewhere that I should use the relativistic mass in the calculation of the centripetal force, i.e.

[itex]F = \frac{\gamma m v^2}{R}[/itex],

but I am not sure why this is the case. Could anyone help?

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# Homework Help: Special relativity, circular motion

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