(a)
The equilibrium position
(a)
Answer to Problem 61AP
The equilibrium position
Explanation of Solution
Write the expression for the potential energy of the particle field system.
Here,
At equilibrium distance, force on the particle become zero or potential energy reaches minimum value.
Write the condition for the equilibrium distance.
Here,
Take derivative of equation (I) with respect to distance get equilibrium position.
Conclusion:
Apply condition of equilibrium given in equation (II) to get
Substitute
Therefore, the equilibrium position
(b)
The depth
(b)
Answer to Problem 61AP
The depth
Explanation of Solution
The depth of the potential well is the potential energy of the particle at equilibrium position.
Write the expression for the depth of the potential well.
Here,
The equilibrium distance
Use equation (I) in (III) to get depth of the potential well.
Substitute
Rearrange above equation to get
Conclusion:
Substitute
Therefore, the depth
(c)
The maximum force along the negative
(c)
Answer to Problem 61AP
The maximum force along the negative
Explanation of Solution
Write the expression for the force acting on the particle along
Here,
Write the condition for the maximum force.
Here,
Conclusion:
Substitute
Differentiate above equation to get derivative of force.
Apply condition of maximum force given in equation (VI) in above equation to get position at which maximum force obtained.
Rearrange above equation to get
Substitute
Here,
Rearrange above equation to get
Substitute
Since the force is along
Therefore, the maximum force along the negative
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Chapter 43 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
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