Helpful Hints for Starting a Difficult Question

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In summary: The magnetic moment of a dipole is given by $$m=\frac{1}{2}\left(\vec m^2-\vec m_0\right).$$Yes. The magnetic moment of a dipole is given by $$m=\frac{1}{2}\left(\vec m^2-\vec m_0\right).$$
  • #1
hidemi
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Homework Statement
If R is the distance from a magnetic dipole, then the magnetic field it produces is proportional to:
A. R^2
B. R
C. 1/R
D. 1/R^2
E. 1/R^3

Ans: E
Relevant Equations
B * ds = u * I
I have no idea how to start this question. Can anyone give me some hints, please? Thanks.
 
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  • #2
hidemi said:
Homework Statement:: If R is the distance from a magnetic dipole, then the magnetic field it produces is proportional to:
A. R^2
B. R
C. 1/R
D. 1/R^2
E. 1/R^3

Ans: E
Relevant Equations:: B * ds = u * I

I have no idea how to start this question. Can anyone give me some hints, please? Thanks.
I would assume it means the distance perpendicular to the dipole's axis.
Two options..
1. Consult your notes or search the net for the formula
2. Work it out from first principles. Draw a diagram. You have the short axis of the dipole, length h say, and some point P distance R off to the side, forming a long thin triangle. If a test pole is placed at P it will be attracted by one end of the dipole and repulsed by the other. How do these forces depend on R? What, approximately, will the net field be?
 
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  • #3
By following your instruction, here's what I got as attached. Let me know if I did it wrong, thank you.
 

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  • #4
hidemi said:
By following your instruction, here's what I got as attached. Let me know if I did it wrong, thank you.
Well done.
 
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  • #5
hidemi said:
By following your instruction, here's what I got as attached. Let me know if I did it wrong, thank you.
You used the Biot-Savart law, but the problem doesn't give you an electric corrent. I think neither Ampere's law nor Biot-Savart law can work in this case as you don't have a current I in the problem statement
 
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  • #6
Anti Hydrogen said:
You used the Biot-Savart law, but the problem doesn't give you an electric corrent. I think neither Ampere's law nor Biot-Savart law can work in this case as you don't have an current I in the problem statement
The spatial dependence of the dipole field does not depend on whether the dipole is generated by a current ##I## or through other means. In fact the spatial dependence of an electric dipole is the same as that of a magnetic dipole.
 
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  • #7
haruspex said:
I would assume it means the distance perpendicular to the dipole's axis.
Does it matter? The magnetic dipolar field due to dipole ##\vec m## is $$\vec B=\frac{\mu_0}{4\pi}\left[\frac{3(\vec m\cdot\hat r)\hat r-\vec m}{r^3}\right].$$
 
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  • #8
kuruman said:
Does it matter? The magnetic dipolar field due to dipole ##\vec m## is $$\vec B=\frac{\mu_0}{4\pi}\left[\frac{3(\vec m\cdot\hat r)\hat r-\vec m}{r^3}\right].$$
what does m represent? the magnetic moment?
 
  • #9
Anti Hydrogen said:
what does m represent? the magnetic moment?
Yes.
 
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Related to Helpful Hints for Starting a Difficult Question

1. What are some strategies for approaching a difficult scientific question?

Some helpful hints for starting a difficult question include breaking it down into smaller parts, brainstorming possible solutions, and seeking input from colleagues or experts in the field. It can also be helpful to take breaks and come back to the question with a fresh perspective.

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