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Page 802: Practice Problems
Suppose the value of the magnetic field is doubled, then the value of radius is halved.
Let the radius of new circular paths are
$r’_{U-238} = dfrac{r_{U-238}}{2}$ and $r’_{U-235} = dfrac{r_{U-235}}{2}$
The new separation between the isotopes is
$d’ = 2 r’_{U-238} – 2r’_{U-235} = cancel{2} dfrac{r_{U-238}}{cancel{2}} – cancel{2} dfrac{r_{U-235}}{cancel{2}} = r_{U-238} – r_{U-235}= dfrac{d}{2}$
Thus if the field is doubled the separation is also halved.
So if the magnetic field is increased the separation decreases.
$r = dfrac{m_p v}{e B} = dfrac{1.673 times 10^{-27} times 6.27 times 10^5}{1.6 times 10^{-19} times 0.45} = 14.6 times 10^{-3}:m = 14.6:mm$
$v=dfrac{|e| B r}{m_e} = dfrac{1.6 times 10^{-19} times 0.0033 times 2.1 times 10^{-2}}{9.11 times 10^{-31}} = 121.7 times 10^5:m/s$