Is Magnetic Susceptibility Always Accurately Represented in Textbooks?

[fayled]

This is defined by M=X_mH.

Using H=(B/u₀)-M to eliminate M gives us M=1/u₀(X_m/1+X_m)B, where B is the total magnetic field.

Now my problem is, my book states that for paramagnetic media, X_m is positive, and for diamagnetic media X_m is negative. Now for paramagnetism, we expect M and B to have the same directions, i.e the constant of proportionality above should be positive - X_m>0 achieves this so it is fine. For diamagnetism however, where M and B have opposite directions, we expect the constant to be negative. If we write the constant as 1/1+1/(X_m) (ignoring the positive u₀), we see that X_m<0 achieves this, but only for X_m between 0 and -1. So what the book is saying doesn't seem to be true all the time. The only thing I can see that could save this is that apparently X_m values are typically of the order of around 10^-5 so this would be correct - but I don't like how the book doesn't mention something that could theoretically happen so would be grateful if somebody could tell me if I'm right or not, thankyou :)

 

[rude man]

B = μ₀H + μ₀M = μ₀H(1 + X_m).
B cannot be negative!

 

[fayled]

We're dealing with vectors though - I'm not sure what that has to do with anything?

 

[fayled]

B = μ₀H + μ₀M = μ₀H(1 + X_m).
B cannot be negative!

We're dealing with vectors though - I'm not sure what that has to do with anything?

Edit: are you possiby claiming this is why X_m is limited between 0 and -1 in terms of the negative values it can take?

 

[nasu]

A perfect diamagnet has a susceptibility of -1.
http://en.wikipedia.org/wiki/Meissner_effect#Perfect_diamagnetism

 

[rude man]

We're dealing with vectors though - I'm not sure what that has to do with anything?

Edit: are you possiby claiming this is why X_m is limited between 0 and -1 in terms of the negative values it can take?

Not only possibly - definitely!
What do vectors have to do with it? B nd H are always collinear.

 

[fayled]

Not only possibly - definitely!
What do vectors have to do with it? B nd H are always collinear.

Why must B and H be collinear though, I'm struggling to see this - it would solve a few other issues I'm having with this topic too. And It's most likely very obvious...

 

[rude man]

B = μH.
B and H are vectors. μ is a scalar.

H is a function of current. The current sets up the H field per Ampere's law or more generally by del x H = j (in the absence of time-varying electric fields). j is current density. (In permanent magnets the currents are "amperian" currents not subject to resistive dissipation).

B is the magnetic field as defined by F = qv x B. B is "generated" by H. In a vacuum, the relation is B = μ₀H. If there is magnetic material present, individual domains will align with the H field (what else could they do? They either align with the H field or stay put, or anti-align in the case of predominantly diamagnetic materials. The domains that stay put average to zero net susceptibility. If most of them line up the susceptibility is high (can be > 1000 in certain paramagnetic substances, like iron).).