
Concept explainers
(a)
ToCalculate: The potential difference between the cylinders.
(a)

Answer to Problem 90P
Explanation of Solution
Given information :
Radii of coaxial
Charge of the inner cylinder =
Charge of the outer cylinder =
Formula used :
Electric potential:
Where, Q is the charge stored and C is the capacitance.
Where,
Calculation:
The potential difference between the cylinders to their charge and capacitance is,
The capacitance of a cylindrical capacitor as a function of its radii a and b and length L:
Conclusion:
The potential difference between the cylinders is
(b)
ToCalculate: The density of the free charge of on the inner cylinder and the outer cylinder.
(b)

Answer to Problem 90P
Explanation of Solution
Given information:
Radii of coaxial conducting thin cylindrical shells =
Charge of the inner cylinder =
Charge of the outer cylinder =
Formula used:
Charge density:
Where, Q is the charge, r is the radius and L is the length of the cylinder.
Calculation:
Surface charge density is:
Conclusion:
The density of the free charge of on the inner cylinder and the outer cylinder are:
(c)
ToCalculate: The bound charge density
(c)

Answer to Problem 90P
Explanation of Solution
Given information :
Radii of coaxial conducting thin cylindrical shells =
Charge of the inner cylinder =
Charge of the outer cylinder =
Formula used :
Bound charge can be expressed as:
Where,
Bound charge density:
Where, A is the area.
Calculation:
Conclusion:
The bound charge density
(d)
ToCalculate: The total stored energy.
(d)

Answer to Problem 90P
Explanation of Solution
Given information:
Radii of coaxial conducting thin cylindrical shells =
Charge of the inner cylinder =
Charge of the outer cylinder =
Formula used:
The energy stored in the capacitor:
Where, Q is the charge and V is the electric potential.
Calculation:
The potential difference between the cylinders is
The total stored energy in terms of the charge stored and the potential difference between the cylinders:
Conclusion:
The total stored energy is,
(e)
ToCalculate: Mechanical work that is required to remove the dielectric cylindrical shell.
(e)

Answer to Problem 90P
Explanation of Solution
Given information:
Radii of coaxial conducting thin cylindrical shells =
Charge of the inner cylinder =
Charge of the outer cylinder =
Formula used:
Work done in terms of potential energy of the system:
Calculation:
The work required to remove the dielectric cylindrical shell in terms of the change in the potential energy of the system:
The potential energy of the system with the dielectric shell in place is,
Conclusion:
Mechanical work that is required to remove the dielectric cylindrical shell is
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Chapter 24 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
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