Concept explainers
(a)
Calculate the voltage V and electric field E.
(a)
Answer to Problem 59P
The voltage V and electric field E are
Explanation of Solution
Calculation:
Consider the following expressions.
And
From the given data, we know that potential depends only on x. Therefore, Laplace’s equation in Cartesian coordinates is given by,
Integrate the above equation with respect to x.
Integrate the above equation with respect to x.
Consider that
Substitute 0 for x and 0 for V in Equation (1).
Consider that
Substitute d for x and
Substitute
Substitute
Calculate the electric field.
Conclusion:
Thus, the voltage V and electric field E are
(b)
Find the expression for
(b)
Answer to Problem 59P
The expression for polarization vector P is
Explanation of Solution
Calculation:
Consider the expression for the polarization.
Here,
Write the expression for electrical susceptibility
Substitute
Substitute
Conclusion:
Thus, the expression for polarization vector P is
(c)
Find the density
(c)
Answer to Problem 59P
The density
Explanation of Solution
Calculation:
Calculate the charge density
Calculate the charge density
Conclusion:
Thus, the density
(d)
Find the expression for the capacitance.
(d)
Answer to Problem 59P
The expression for capacitance is
Explanation of Solution
Calculation:
Calculate the electric field.
Calculate the voltage of the capacitor.
Consider the expression for the capacitance.
Substitute
Conclusion:
Thus, the expression for capacitance is
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Chapter 6 Solutions
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