Concept explainers
A square filamentary differential current loop, dL on a side, is centered at the origin in the z = 0 plane in free space. The current I flows generally in the aD direction, (a) Assuming that r dL, and following a method similar to that in Section 4.7, show that
(b) Show that
The square loop is one form of a magnetic dipole.
(a)
To prove:
Explanation of Solution
Given info:
The centre of the square differential current loop origin in the plane z = 0. The current I is flowing in the
Calculation:
We assume that
Consider the figures below y-displaced elements. Considering the observation point is far than the lines
Figure 1
Figure 2
The net potential can be written as,
From figure (1) and figure (2) we can take,
We know that
By substituting the values in the above equation, we get,
We can write
We have considered
Thus, the relation is proved.
(b)
To prove:
Explanation of Solution
Given info:
The centre of the square differential current loop origin in the plane z = 0. The current I is flowing in the
Calculation:
We know that
Substitute
Now we have
Thus, the relation is proved.
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Chapter 7 Solutions
Engineering Electromagnetics
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