Magnetic dipole at the centre of a sphere

[shubham agn]

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?

 

[Philip Wood]

(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.

 

[shubham agn]

(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.

 

[Philip Wood]

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?

But the answer does not match the correct answer.

And what was your answer?

 

[shubham agn]

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.

 

[Meir Achuz]

You have to be more careful in relating B and H to D and E. Is your "magnetic field" B or H?