Magnetic dipole at the centre of a sphere

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Discussion Overview

The discussion centers on the calculation of the magnetic field inside a sphere containing a point magnetic dipole at its center, specifically addressing the methods and assumptions involved in deriving the field. The scope includes theoretical reasoning and mathematical modeling related to magnetism and dipole fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes a method of calculating the magnetic field by drawing an analogy between the magnetic dipole and an electric dipole, suggesting to replace parameters accordingly.
  • Another participant questions the relevance of the sphere in the calculation and suggests focusing on the field strength at a distance from the dipole itself.
  • A participant mentions that the magnetic dipole will magnetize the sphere, creating an additional field that must be considered in the net field calculation.
  • There is a request for clarification on whether the term "magnetic field" refers to B or H, indicating a need for careful distinction in the context of the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the sphere and the method used to calculate the magnetic field. There is no consensus on the correct approach or the validity of the proposed method.

Contextual Notes

Participants have not fully resolved the assumptions regarding the relationship between the magnetic field and the parameters involved, nor have they clarified the implications of the sphere's presence in the calculations.

shubham agn
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The problem is as follows: There is a point magnetic dipole embedded at the center of a sphere (radius R) of linear magnetic material of permeability μ. What is the magnetic field inside the sphere?
I know that this problem has been solved in many books.But I am trying a different method. Since the magnetic field of a magnetic dipole takes the same form as electric field of an electric dipole, I calculated the electric field inside a sphere (of linear dielectric material of permittivity ε) having a point electric dipole embedded at the center.
And then just replaced ε by 1/μ and the electric dipole moment 'p' by the magnetic dipole moment 'm' and of course epsilon naught by one over mu naught. But the answer does not match the correct answer.
Is this method of mine wrong?
 
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(1) Do you mean the field at a distance R from the centre of the dipole?
(2) Are you assuming (as usual) that the linear dimensions of the dipole are much less than R?
(3) It would probably help if you posted your own result.
 
Philip Wood said:
(1) Do you mean the field at a distance R from the centre of the dipole?
(2) Are you assuming (as usual) that the linear dimensions of the dipole are much less than R?
(3) It would probably help if you posted your own result.
First, thanks for your reply!
The question is to find the field at a distance r <R from the dipole. And yes the dipole is assumed to be a point dipole so its linear dimensions are small compared to R.
 
Still can't see the relevance of the sphere. Why not just find the field strength at distance r from (the centre of) the dipole?
shubham agn said:
But the answer does not match the correct answer.
And what was your answer?
 
Philip Wood said:
Still can't see the relevance of the sphere. Why not just find the field strength at distance r from (the centre of) the dipole?

And what was your answer?
The magnetic dipole will magnetize the sphere. This magnetization will create a field of its own. We need to find the net field, that is the resultant field due the dipole and the magnetization of the sphere. My answer is almost the same as that given in Griffiths text except that in the denominator of the second term mu naught and μ are interchanged in my answer.
 
You have to be more careful in relating B and H to D and E. Is your "magnetic field" B or H?
 

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