Problem 20.12

จาก \(ΣW_{NC}= \Delta E\)

\(0 = \Delta K + \Delta U\)

\(\Delta K = -\Delta U\)

\(mv^{2} = -(e)(-\Delta V)\frac{1}{2}\)

\(v =\sqrt{\frac{2e\Delta V}{m}}\)

จาก \(|\vec{F}_{B}|= |q\vec{v}\times \vec{B}|\)

\(m\frac{v^{2}}{r}= ev|\vec{B}|\)

\(r =\frac{mv}{e|\vec{B}|}\)

\(r =\frac{1}{|\vec{B}|}\sqrt{\frac{2m\Delta V}{e}}\)

\(r = km; k =\frac{1}{|\vec{B}|}\sqrt{\frac{2\Delta V}{e}}\)

\(\therefore \frac{R}{r}=\sqrt{\frac{2m}{m}}\)

\(R =2r \;\blacksquare\)