- #1
Demon117
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Homework Statement
What is the motion of the guiding center of a particle in the field of a straight current carrying wire? What happens to the particle energy?
Homework Equations
The field is tangential to the Amperian loop, so the magnetic field is simply:
\oint B\cdot dl = \mu_{o}I \Rightarrow \vec{B}=\frac{\mu_{o}I}{2\pi r}\hat{\phi}
The Attempt at a Solution
The drift velocity will be due to the curvature of the magnetic field and also the grad-B drift. So we need to compute the Grad of the \phi component of the field, which is simply
\nabla B_{\phi} = -\frac{\mu_{o}I}{2\pi r^{2}}\hat{r}
At this point I think I know what I should do, and that is to calculate \vec{B}\times \nabla B, such that
\vec{v_{d}}=1/2 v_{\bot}r_{L}(\vec{B}\times \nabla B)/B^{2}
where r_{L} is the larmor radius. Does this look correct, am I missing anything?
