Concept explainers
(a)
The voltage
Answer to Problem 6.39P
The voltage
Explanation of Solution
Calculation:
The general solution of Laplace's equation is written as,
Here,
Substitute
Equation (2) is simplified as,
Substitute
Equation (4) is simplified as,
Subtracting equation (5) from equation (3) as,
By solving equation (6) the values of
Substitute
Conclusion:
Therefore, the voltage
(b)
The electric field
Answer to Problem 6.39P
The electric field intensity
Explanation of Solution
Calculation:
The electric field
Here,
Differentiate the equation (7) with respect to
Substitute
Conclusion:
Therefore, the electric field intensity
(c)
The electric field displacement
Answer to Problem 6.39P
The electric field displacement
Explanation of Solution
Calculation:
The electric field displacement
Here,
Substitute
Conclusion:
Therefore, the electric field displacement
(d)
The charge surface density
Answer to Problem 6.39P
The charge surface density is
Explanation of Solution
Calculation:
The charge surface density
Here,
Substitute
Conclusion:
Therefore, the charge surface density is
(e)
The charge
Answer to Problem 6.39P
The charge
Explanation of Solution
Calculation:
The charge
Here,
Substitute
Conclusion:
Therefore, the charge
(f)
The voltage
Answer to Problem 6.39P
The voltage
Explanation of Solution
Calculation:
The general solution of Laplace's equation is written as,
Substitute
Equation (13) is simplified as,
Substitute
Equation (15) is simplified as,
Subtracting equation (16) from equation (14) as,
By solving equation (17) the values of
Substitute
The electric field
Differentiate the equation (18) with respect to
Substitute
The electric field displacement
Substitute
The charge surface density
Substitute
The charge
Substitute
Conclusion:
Therefore, the voltage
(g)
The total charge on the lower plane and the capacitance between the planes.
(g)
Answer to Problem 6.39P
The total charge on the lower plane is
Explanation of Solution
Calculation:
The total charge
Here,
Substitute
The potential difference
Substitute
The capacitance
Substitute
Conclusion:
Therefore, the total charge on the lower plane is
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Chapter 6 Solutions
Engineering Electromagnetics
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