Magnetic power balance on an expanding circular guide
= Magnetic power balance on an expanding circular guide
For laboratory <velocity> $v\hat r+w\hat\theta$ and field $B\hat z$, $F_{B,r}=qBw$ and $F_{B,\theta}=-qBv$. Their <powers> are opposite. The field-dependent guide-reaction <power> is $-qBvw$; the total ideal radial reaction for bead <mass> $m_b$ and constant expansion <speed> additionally contributes the ordinary centripetal term $-m_bvw^2/R$.