Helpful Hints for Starting a Difficult Question

[hidemi]

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.

 

[haruspex]

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?

 

[hidemi]

By following your instruction, here's what I got as attached. Let me know if I did it wrong, thank you.

 

[haruspex]

By following your instruction, here's what I got as attached. Let me know if I did it wrong, thank you.

Well done.

 

[Anti Hydrogen]

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

 

[kuruman]

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.

 

[kuruman]

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 $$\vec B=\frac{\mu_0}{4\pi}\left[\frac{3(\vec m\cdot\hat r)\hat r-\vec m}{r^3}\right].$$

 

[Anti Hydrogen]

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?

 

[kuruman]

what does m represent? the magnetic moment?

Yes.