Magnetic Field around a dipole calculation

In summary, the conversation is about understanding the transition from equation 8.20 to 8.21a in the book Elements of Electromagnetics. The person discussing the topic suggests subbing in dl=a.d∅.a∅ and integrating ∅ between 0 and 2pi, but realizes this is incorrect. They mention the assumption that r>>a and ask for help. However, they later find an explanation on Google Books.
  • #1
crystalbrite
5
0

Homework Statement


I've attached a page from the book Elements of Electromagnetics.

I was wondering how he gets from eq.8.20 to eq.8.21a.

What I would have done is sub in dl=a.d∅.a∅ and integrate ∅ between 0 and 2pi.

This would then give you A=[(2.μ0.I.pi.a)/(4.pi.r)].a∅

This is obviously wrong because it's not what he got. He does make an assumption that r>>a so maybe i have to do something with that.

Any help would be much appreciated

Thanks
 
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  • #2
I think i forgot the attachment
 

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  • #3
Its ok, i found the explanation in a book on google books. Its a bit long and tedious.

I guess no one here would be able to understand it which is why i got no reply. Oh well...
 

FAQ: Magnetic Field around a dipole calculation

What is a dipole?

A dipole is a pair of equal and opposite charges separated by a small distance. It can also refer to a pair of magnetic poles with opposite orientation.

How do you calculate the magnetic field around a dipole?

The magnetic field around a dipole can be calculated using the equation B = μ0M/4πr^3, where B is the magnetic field, μ0 is the permeability of free space, M is the dipole moment, and r is the distance from the dipole.

What factors affect the strength of the magnetic field around a dipole?

The strength of the magnetic field around a dipole is affected by the magnitude of the dipole moment, the distance from the dipole, and the orientation of the dipole relative to the observation point.

Can the magnetic field around a dipole be negative?

No, the magnetic field around a dipole cannot be negative. It is always either positive or zero, depending on the direction and magnitude of the dipole moment.

How is the magnetic field around a dipole different from the magnetic field around a single charge?

The magnetic field around a dipole has a more complex and varying pattern compared to the simpler and more uniform magnetic field around a single charge. Additionally, the magnetic field around a dipole has both a radial and a tangential component, while the magnetic field around a single charge only has a radial component.

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