Magnetic susceptibility and relative permeability

In summary: Best wishes.In summary, the conversation discusses deriving the formula for magnetic susceptibility, χm=μr-1, using relevant equations such as M=Xm.H, μ=μrμ0, β=μH, and βo=μoH. The final solution involves substituting M=χmH into B=μ0(H+M) and factoring out the H to get the final formula χm=1-μr.
  • #1
Marwa
6
1

Homework Statement


find the derivation of
χm=μr-1
where Xm is the magnetic susceptibility and μ is the relative permeability.

Homework Equations


M=Xm.H
M is the magnetization,H is the magnetic field
μr=μ/μo
where μo is the permeability of a vacuum,


The Attempt at a Solution


I don't know how to start ,I know some equations related to magnetic properties but i cannot connect them to each other to find the derivation.
 
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  • #2
Hello Marwa,

Welcome to Physics Forums! :smile:

For convenience, I've retyped in your problem.

Derive the formula,
[tex] \chi_m = \mu_r - 1 [/tex]

Relevant equations:
[tex] \mathrm{\textbf{M}} = \chi_m \mathrm{\textbf{H}} [/tex]
[tex] \mu = \mu_r \mu_0 [/tex]
I'm pretty sure you will need one or two more relevant equations.
Can you find any relevant equations that relate to the magnetic field, [itex] \mathrm{\textbf{B}} [/itex]?
.
.
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  • #3
Relevant equations:
β=μH

βo=μoH

μr=μ/μo

β = μoH+ μoM

M=Xm.H
 
  • #4
Marwa said:
Relevant equations:
β=μH

βo=μoH

μr=μ/μo

β = μoH+ μoM

M=Xm.H

Okay, with these relevant equations,
[tex] \mathrm{\textbf{M}} = \chi_m \mathrm{\textbf{H}} [/tex]
[tex] \mu = \mu_r \mu_0 [/tex]
[tex] \mathrm{\textbf{B}} = \mu \mathrm{\textbf{H}}[/tex]
[tex] \mathrm{\textbf{B}} = \mu_0 \left( \mathrm{\textbf{H}} +\mathrm{\textbf{M}} \right)[/tex]
you have enough to show that
[tex] \chi_m = \mu_r - 1. [/tex]
What have you tried so far?
 
  • #5
I have tried :

M=Xm.H
Xm=M/H
Xm=Mμ/B
as H=B/μ
and B=μo(H+M)
Xm=(M.μ)/μo(H+M)
so Xm=μr.M/(H+M)
 
  • #6
Marwa said:
I have tried :

M=Xm.H
Xm=M/H
Xm=Mμ/B
as H=B/μ
and B=μo(H+M)
Xm=(M.μ)/μo(H+M)
so Xm=μr.M/(H+M)

Try substituting
M = χmH
into
B=μ0(H+M)​
Then factor the H.
 
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  • #7
I got it:

B=μo(H+M)
and M=XmH
B=μo(H+XmH)
B=μoH(1+Xm)
so μH=μoH(1+Xm)
μ/μo=μr
Xm=1-μr

Thank you.
 
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  • #8
DERIVE THE RELATIONSHIP B = μ0(H + M)
 
  • #9
Inusa Adamu Gurai said:
DERIVE THE RELATIONSHIP B = μ0(H + M)
I need the same,
Help me of you find it
 
  • #10
Arun said:
I need the same,
Help me of you find it
Hello @Arun,

I suggest starting a new thread if you need help on this. Be sure to use the automatic template (problem statement, relevant equations, attempted solution, and so forth).
 

FAQ: Magnetic susceptibility and relative permeability

What is magnetic susceptibility?

Magnetic susceptibility is a measure of the degree to which a material can be magnetized in the presence of an external magnetic field. It is a dimensionless quantity that indicates the extent to which a material is attracted to or repelled by a magnetic field.

How is magnetic susceptibility measured?

Magnetic susceptibility is typically measured using a device called a magnetic susceptibility balance. This device consists of a magnetic field generator and a sample holder. The sample is placed in the holder and the device measures the force exerted on the sample by the magnetic field, which is used to calculate the magnetic susceptibility.

What is relative permeability?

Relative permeability is a measure of how easily a material can be magnetized compared to a vacuum. It is the ratio of the magnetic permeability of a material to the magnetic permeability of a vacuum. Materials with a higher relative permeability are more easily magnetized in the presence of a magnetic field.

How is relative permeability related to magnetic susceptibility?

Relative permeability and magnetic susceptibility are closely related. In fact, magnetic susceptibility is often used as a way to measure relative permeability. The higher the magnetic susceptibility of a material, the higher its relative permeability will be.

What factors affect magnetic susceptibility and relative permeability?

The magnetic properties of a material, including magnetic susceptibility and relative permeability, are affected by a variety of factors such as temperature, pressure, and the type and strength of the external magnetic field. Additionally, the chemical composition and atomic structure of the material also play a role in determining its magnetic properties.

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