= Solution
With $V=+20\,\mathrm V$ in the outer-minus-inner convention, $\eta=\ln1.5=0.405465$ and the radial <electric field> at the orbit is $E_r=-986.52\,\mathrm{V\,m^{-1}}$. The signed roots are
$$
u_\pm=\frac{-eBr\pm\sqrt{e^2B^2r^2+4meV/\eta}}{2m}.
$$
Using the <proton> <mass> and charge gives
$$
\boxed{u_+=4.88\times10^4\,\mathrm{m\,s^{-1}},\qquad
u_-=-9.67\times10^4\,\mathrm{m\,s^{-1}}.}
$$
The <speeds> are therefore $48.8$ and $96.7\,\mathrm{km\,s^{-1}}$, in opposite senses of rotation. Both are nonrelativistic. The slower counterclockwise orbit has an outward magnetic <force>; the faster clockwise orbit has an inward magnetic <force>. Reversing $\mathbf B$ interchanges the senses, while reversing the electrode polarity changes the quadratic and may eliminate real orbits; its sign must therefore be specified.
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