Concept explainers
Consider the basic image problem of a point charge q at z=d, suspended over an infinite conducting plane at z=0. Eq. (10) in chapter 2 to find E and D everywhere at the conductor surface as functions of cylindrical radius p. (b) Use your from part a to find the charge density, and the total induced charge on the conductor.
(a)
The expression for E and D as a function of cylindrical radius
Answer to Problem 5.20P
The required expressions are:
Explanation of Solution
Given Information:
The point charge q is at
Calculation:
Let the point charge and conducting plane are in cylindrical coordinate system. Consider a point
So, the electric filed intensity:
The displacement field:
Conclusion:
The required expressions are:
(b)
The charge density and total induced charge on the conductor.
Answer to Problem 5.20P
The charge density is
Explanation of Solution
Given Information:
The point charge q is at
Calculation:
The conducting plate is xy plane.
So, the unit normal vector:
So, the charge density:
The induced charge,
Conclusion:
The charge density is
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Chapter 5 Solutions
Engineering Electromagnetics
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