Concept explainers
(a)
The field into cylindrical coordinates.
Answer to Problem 1.19P
The field into cylindrical coordinates is
Explanation of Solution
Concept used:
Write the expression for the
Here
Write the expression for the
Here,
Write the expression for the
Here,
Calculation:
The expression for the field into rectangular coordinates is
The expression for the field in the
Substitute
Here,
The expression for the field in the
Substitute
The expression for the field in the
Substitute
The expression for the field in of the cylindrical coordinate system can be written as the sum of the all three component of the cylindrical coordinate system.
Substitute
Simplify further.
Conclusion:
Thus, the field into cylindrical coordinates is
(b)
The field into rectangular coordinates.
Answer to Problem 1.19P
The expression for the field into rectangular coordinates is
Explanation of Solution
Given:
The expression for the field in spherical coordinate
Concept used:
Write the expression for the radius of the spherical system in term of rectangular system.
Here
Write the expression for the angle between
Write the expression for the angle between
Calculation:
The expression for
By Pythagoras theorem
By Pythagoras theorem
By Pythagoras theorem
The expression for the field in the
Here,
Substitute
The expression for the field in the
Here,
Substitute
The expression for the field in the
Here,
Substitute
The expression for the field in of the rectangular coordinate system can be written as the sum of the all three component of the rectangular coordinate system.
Substitute
Simplify further.
Conclusion:
Thus, the expression for the field into rectangular coordinates is
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Chapter 1 Solutions
Engineering Electromagnetics
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