Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
Textbook solutions

All Solutions

Page 802: Practice Problems

Exercise 28
Step 1
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Radius of the circular orbit is inversely proportional to the magnetic field.

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.

Result
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See Explanation.
Exercise 29
Step 1
1 of 1
The radius of proton’s circular path that moves with the speed $6.27times 10^5::m/s$, perpendicular to the magnetic field of $0.45:T$ is given by

$r = dfrac{m_p v}{e B} = dfrac{1.673 times 10^{-27} times 6.27 times 10^5}{1.6 times 10^{-19} times 0.45} = 14.6 times 10^{-3}:m = 14.6:mm$

Exercise 30
Step 1
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The speed of the electron that moves in a circular orbit of radius $r=2.1:cm = 2.1 times 10^{-2}:m$ and perpendicular to the magnetic field of $B =0.0033:T$ is given by

$v=dfrac{|e| B r}{m_e} = dfrac{1.6 times 10^{-19} times 0.0033 times 2.1 times 10^{-2}}{9.11 times 10^{-31}} = 121.7 times 10^5:m/s$

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