- #1

enerieire

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μ=½B(R^3)

I am considering a sphere of radius R, with B its magnetic field. Who is μ?

Thanks

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- Thread starter enerieire
- Start date

In summary, μ is the magnetic moment of a sphere with magnetic field B. It comes from the classical definition of the magnetic moment for a charge distribution.

- #1

enerieire

- 8

- 0

μ=½B(R^3)

I am considering a sphere of radius R, with B its magnetic field. Who is μ?

Thanks

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- #2

Baluncore

Science Advisor

2023 Award

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B is measured in tesla = N⋅m

Multiply B by m

We know force; N = kg⋅m⋅s

So; μ = (kg⋅m⋅s

μ = m

Which has exactly the same dimensions as;

See tables; https://en.wikipedia.org/wiki/SI_derived_unit

magnetic moment = weber⋅meter = m

So μ is the magnetic moment.

- #3

enerieire

- 8

- 0

Starting from the classical definition for the magnetic moment for a charge distribution

μ=∑qr

I don't find an answer

Thanks

- #4

weirdoguy

- 1,101

- 1,035

enerieire said:Starting from the classical definition for the magnetic moment for a charge distribution

μ=∑qr

Are you sure that is the definition of

- #5

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- #6

Baluncore

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2023 Award

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There are many well trodden paths through this field. But the OP equation seems to be one or two steps off the path.

I agree we need more context to find the path again.

Maybe page 2 of this article will help; http://ccmc.gsfc.nasa.gov/RoR_WWW/presentations/Dipole.pdf

I quote:

The first equation of the dipole field in spherical polar coordinates (r,θ,φ)

is; B = 2 M cos θ / r^{3}

where M is the dipole moment, which can be positive or negative.

From eqn (1) we get; M = ½ B r^{3} / cos θ

But on the dipole axis θ = 0, so; Cos θ = 1.

So; M = ½ B r^{3}

The text box in the bottom corner gives the explanation and;

μ = 4π M / μ_{o} = M x 10^{7}.

I agree we need more context to find the path again.

Maybe page 2 of this article will help; http://ccmc.gsfc.nasa.gov/RoR_WWW/presentations/Dipole.pdf

I quote:

The first equation of the dipole field in spherical polar coordinates (r,θ,φ)

is; B = 2 M cos θ / r

where M is the dipole moment, which can be positive or negative.

From eqn (1) we get; M = ½ B r

But on the dipole axis θ = 0, so; Cos θ = 1.

So; M = ½ B r

The text box in the bottom corner gives the explanation and;

μ = 4π M / μ

Last edited:

A magnetic dipole is a type of magnet that has two poles, a north and a south, just like a traditional bar magnet. These poles create a magnetic field that can interact with other magnets or magnetic materials.

The strength of a magnetic dipole is measured by its magnetic moment, denoted by the symbol μ. This is a vector quantity that takes into account the strength of the poles as well as the distance between them.

The magnetic dipole moment can be calculated by multiplying the strength of the poles (magnetic pole strength) by the distance between them. The resulting value is then multiplied by a constant, known as the permeability of free space, to give the final value of μ.

The magnetic dipole originates from the movement of charged particles, such as electrons, within a magnet. These particles create a tiny current loop that produces a magnetic field, resulting in a magnetic dipole.

The magnetic dipole has many applications in everyday life, such as in compasses for navigation, electric motors, and magnetic storage devices like hard drives. It is also used in scientific research and medical imaging techniques such as magnetic resonance imaging (MRI).

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