Concept explainers
(a)
Value of H on the z -axis.
Answer to Problem 7.4P
Explanation of Solution
Given:
The given configuration is
I =
Range is
Calculation:
The figure for the loop structures carrying current can be drawn as below:
The equation for H because of small current element 'Idl' will be
The
The differential expression for magnetic field intensity will be
The vector starting from current loop to the concerned point at a height 'h' will be
The equation for H because of small current element 'Idl' will be
The differential expression for magnetic field intensity will be
Because of symmetry, the magnetic field is there only in the direction of
Integrating over an azimuthal angle
The total magnetic field due to upper ring will be
The total magnetic field due to lower ring will be
As the magnetic fields are linear, therefore, the magnetic field at point P will be the sum of both.
That is,
The above expression is the value of magnetic field on the positive side of the z axis.
The total magnetic field an any point on the z axis between the range
(b)
To plot:
The graph of
Explanation of Solution
Given:
The given configuration is
I =
Calculation:
Substituting I = 1A and manipulating the equation for z/a, the modulus of total field will be
Put
Therefore, the plot will be
(c)
To plot:
The graph of
Explanation of Solution
Given:
The given configuration is
I =
Calculation:
Substituting I = 1A and manipulating the equation for z / a, the modulus of total field will be
Put
Therefore, the plot will look li
The most uniform field is obtained when
(d)
To plot:
The graph of
Answer to Problem 7.4P
The most uniform field is obtained when
Explanation of Solution
Given:
The given configuration is
I =
Calculation:
Substituting I = 1A and manipulating the equation for z/a, the modulus of total field will be
Put
Therefore, the plot will look like
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Chapter 7 Solutions
Loose Leaf For Engineering Electromagnetics
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