Concept explainers
(a)
The potential on the
(a)
Answer to Problem 88P
The potential on the
Explanation of Solution
Formula used:
The expression for potential due to the ring is given by,
The potential due to the ring is the sum of the charges due to charge on the left and right is given by,
Calculation:
The potential due to the ring on the left side is written as,
The potential due to the ring on the right side is written as,
The potential due to the ring is calculated as,
Therefore, the potential on the
(b)
The position for the minimum value of
(b)
Answer to Problem 88P
The position for the minimum value of
Explanation of Solution
Calculation:
Differentiatethe potential of the ring.
Solving for
Evaluating
Evaluating this expression for
The above expression implies
Conclusion:
Therefore,
(c)
The potential for
(c)
Answer to Problem 88P
The potential for
Explanation of Solution
Formula used:
The Taylor series expansion of
Calculation:
For
The potential is calculated as,
Conclusion:
Therefore,the potential for
(d)
The angular frequency of oscillation.
(d)
Answer to Problem 88P
The angular frequency of oscillation is
Explanation of Solution
Formula used:
The expression for the angular frequency of oscillation of a simple harmonic oscillator is given by,
The expression for the potential energy is given by,
Calculation:
The energy is calculated as,
Here,
The angular frequency is then calculated as,
Conclusion:
Therefore,the angular frequency of oscillation is
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Chapter 23 Solutions
Physics for Scientists and Engineers
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