Concept explainers
(a)
The voltage
Answer to Problem 6.34P
The final voltages are:
Explanation of Solution
Calculation:
The Poisson's equation is defined for
The Poisson's equation is written as,
Here,
Integrate the equation (1) with respect to
The Laplace's equation is written as,
Integrate the equation (3) with respect to
Substitute
Simplified the equation (5) as,
Equation (3) is multiplied with
If equation (6) and equation (7) is equal, then it is written as,
Simplified the equation (8) as,
Substitute
Integrate the equation (2) with respect to
Integrate the equation (9) with respect to
Substitute
Equation (12) is simplified as,
Substitute
Substitute
If equation (13) and equation (14) is equal, then it is written as,
Substitute
Substitute
Substitute
Conclusion:
Therefore, the final voltages are
(b)
The electric field intensity.
Answer to Problem 6.34P
The electric field
Explanation of Solution
Calculation:
Differentiate the equation (16) with respect to
Differentiate the equation (17) with respect to
The electric field intensity
Here,
Substitute
The electric field intensity
Substitute
Conclusion:
Therefore, the electric field
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Chapter 6 Solutions
Engineering Electromagnetics
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