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- Homework Statement
- I am trying to solve for the velocity of a relativistic particle in a magnetic field using magnetic force (F = q(v x B)) and F = dp/dt (where p = ɣmv) and equating the two equations to each other. However, I stuck on how to isolate v in this setup.

- Relevant Equations
- F = dp/dt = d(ɣmv)/dt

F = q(v x B)

ɣ = 1/sqrt(1-(v/c)^2)

d(ɣmv)/dt = qvB

(dɣ/dt)mv + ɣm(dv/dt) = qvB

Substituting gamma in and using the chain rule, it ends up simplifying to the following:

ɣ^3*m(dv/dt) = qvB

Now, I am confused on how to solve for v.

(dɣ/dt)mv + ɣm(dv/dt) = qvB

Substituting gamma in and using the chain rule, it ends up simplifying to the following:

ɣ^3*m(dv/dt) = qvB

Now, I am confused on how to solve for v.