Concept explainers
(a)
The rate of change of radius
(a)
Answer to Problem 28P
The rate of change of radius
Explanation of Solution
Write the expression to obtain the kinetic energy of the particle.
Here,
Write the expression to obtain the rate of change of energy.
Here,
Substitute
Write the expression to obtain the speed of the particle.
Here,
Substitute
Further solve the above equation.
Therefore, the rate of change of radius
(b)
The comparison of path of the proton in figure 29.16a with the result in part (a).
(b)
Answer to Problem 28P
The path of the proton in figure 29.16a is unrealistic according to the result in part (a).
Explanation of Solution
Consider equation (II).
From the above expression the rate of change of radius with time is inversely proportional to the radius
In case of the figure 29.16a, the spiral path of the proton is equally spaced throughout.
Therefore, the path of the proton in figure 29.16a is unrealistic according to the result in part (a).
(c)
The rate of change of radial position before the proton leaves the cyclone.
(c)
Answer to Problem 28P
The rate of change of radial position before the proton leaves the cyclone is
Explanation of Solution
Conclusion:
Substitute
Therefore, the rate of change of radial position before the proton leaves the cyclone is
(d)
The increase in radius of the path of the proton during its last full revolution.
(d)
Answer to Problem 28P
The increase in radius of the path of the proton during its last full revolution is
Explanation of Solution
Write the expression to obtain the increase in radius of the path of the proton during its last full revolution.
Here,
Write the expression to obtain the time required to complete one full orbit revolution by the proton.
Here,
Conclusion:
Substitute,
Substitute
Therefore, the increase in radius of the path of the proton during its last full revolution is
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Chapter 29 Solutions
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