Concept explainers
(a)
To show: The energy associated with a single
(a)
Answer to Problem 23P
The energy associated with a single conducting sphere is
Explanation of Solution
Given info: The radii of two conducting sphere is
Write the expression to calculate the capacitance of a sphere of radius
Here,
Write the expression to calculate the potential difference.
Here,
Write the expression to calculate the energy stored in the capacitor.
Substitute
Conclusion:
Therefore, the energy associated with a single conducting sphere is
(b)
The total energy of the system of two spheres in term of
(b)
Answer to Problem 23P
The total energy of the system of two spheres in term of
Explanation of Solution
Given info: The radii of two conducting sphere is
Write the expression to calculate the capacitance of a sphere of radius
Write the expression to calculate the total energy of the system of two sphere.
Substitute
The sum of charge of both sphere are,
Substitute
Thus, the total energy of the system of two spheres in term of
Conclusion:
Therefore, the total energy of the system of two spheres in term of
(c)
The value of
(c)
Answer to Problem 23P
The value of
Explanation of Solution
Given info: The radii of two conducting sphere is
The total energy of the system of two spheres in term of
Differentiate the above equation with respect to
Conclusion:
Therefore, the value of
(d)
The value of
(d)
Answer to Problem 23P
The value of
Explanation of Solution
Given info: The radii of two conducting sphere is
The value of
The sum of charge of both sphere are,
Substitute
Conclusion:
Therefore, the value of
(e)
The potential of each sphere.
(e)
Answer to Problem 23P
The potential of each sphere is
Explanation of Solution
Given info: The radii of two conducting sphere is
Write the expression to calculate the potential of first sphere.
Substitute
Write the expression to calculate the potential of second sphere.
Substitute
Thus, the potential of each sphere is
Conclusion:
Therefore, the potential of each sphere is
(f)
The potential difference between the spheres.
(f)
Answer to Problem 23P
The potential difference between the spheres is zero.
Explanation of Solution
Given info: The radii of two conducting sphere is
The potential difference is,
Substitute
Conclusion:
Therefore, the potential difference between the spheres is zero.
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Chapter 25 Solutions
Physics for Scientists and Engineers with Modern Physics
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