Concept explainers
(a)
ToFind: Expressions for the electric field and energy density as a function of the distance
(a)
Answer to Problem 44P
Explanation of Solution
Given information :
Radius of the wire =
Length of the wire =
Charge =
Inner radius of cylindrical shell =
Length of the cylindrical shell =
Charge =
Formula used :
From Gauss’s law:
Where, E electric field,
Energy density is given by:
Calculation:
Using Gauss’s law, find the electric field for cylindrical surfaces of radii
For
For
The energy density in the region
For
Because
Conclusion:
Electric field
Energy density
(b)
ToCalculate: The amount ofenergy that resides in a region between the conductors that has a radius
(b)
Answer to Problem 44P
Explanation of Solution
Given information:
Radius of the wire =
Length of the wire =
Charge =
Inner radius of cylindrical shell =
Length of the cylindrical shell =
Charge =
Formula used:
The energy residing in a cylindrical shell between the conductors of radius
Calculation:
Conclusion:
The amount ofenergy is:
(c)
To Calculate: The total energy stored in the capacitor.
(c)
Answer to Problem 44P
Explanation of Solution
Given information:
Radius of the wire =
Length of the wire =
Charge =
Inner radius of cylindrical shell =
Length of the cylindrical shell =
Charge =
Formula used:
Energy stored in the capacitor:
Where, C is the capacitance and V is the potential difference.
Calculation:
Integrate
Conclusion:
The total energy stored in the capacitor is:
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Chapter 24 Solutions
Physics for Scientists and Engineers, Vol. 3
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