Concept explainers
(a)
The speed with which the
(a)
Answer to Problem 126P
The speed with which the
Explanation of Solution
The kinetic energy gained by the ion must be equal to the potential energy lost.
Write the equation for the conservation of energy.
Here,
Write the equation for
Here,
Write the equation for
Here,
The charge of the ion is equal to
Replace
Put equations (II) and (III) in equation (I).
Here,
Write the relation for the speed of
Here,
Write the relation for the speed of
Here,
Take the ratio of the above two equations.
The mass of
Substitute
Conclusion:
It is given that the speed of the
Substitute
Therefore, the speed with which the
(b)
The sketch of the trajectory of
(b)
Answer to Problem 126P
The sketch of the trajectory of
Explanation of Solution
In a velocity selector, for an ion with speed
Write the equation for the magnetic force.
Here,
In the velocity selector,
Conclusion:
Thus, the sketch of the
(c)
The diameter of the path of
(c)
Answer to Problem 126P
The diameter of the path of
Explanation of Solution
The charge of the
Write the equation for the magnitude of the magnetic force on ions using equation (V).
Here,
The magnetic force provides the centripetal force needed for the circular motion of the ions.
Write the relationship between the magnetic force and the centripetal force.
Here,
Write the equation for the magnitude of the centripetal force on ions.
Here,
Write the equation for the radius of a circle.
Here,
Put the above equation in equation (VIII).
Put equations (VI) and (IX) in equation (VII).
Since
Write the relationship between the diameters of the paths of
Here,
Rewrite the above relationship for
Conclusion:
Substitute
Therefore, the diameter of the path of
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Chapter 19 Solutions
Physics
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