Sign of g-factor Value: Is It Positive or Negative?

[Amith2006]

Homework Statement

1)I have a doubt regarding the sign of g factor value.
In Wikipedia the g-factors are given as:
Orbital g-factor
Mu(L) = g(L)[Mu(B)L]/h_bar
Where g(L)=-1 is the orbital g factor
Spin g-factor
Mu(S) = g(S)[Mu(B)S]/h_bar
Where g(S)=-2 is the spin g factor
Lande g-factor
Mu(J) = g(J)[Mu(B)J]/h_bar
Where g(J) is the spin g factor

But in my book it is given as follows:
Orbital g-factor
Mu(L) = -g(L)[Mu(B)L]/h_bar
Where g(L)=1 is the orbital g factor
Spin g-factor
Mu(S) = -g(S)[Mu(B)S]/h_bar
Where g(S)=2 is the spin g factor
Lande g-factor
Mu(J) = g(J)[Mu(B)J]/h_bar
Where g(J) is the spin g factor

Which is correct? Is the g factor positive or negative? Also, in Wikipedia it is given that the g-factor value for electrons, neutrons and muon is negative while it is positive for protons. I think they mean spin g-factor here.

Homework Equations

The Attempt at a Solution

 

[Jhero]

The g-factor is a dimensionless quantity that describes the strength of the magnetic moment of a particle in an external magnetic field. The correct sign of the g-factor depends on the convention used and can be positive or negative. It is important to note that the g-factor is not a fundamental property of a particle, but rather a result of its interactions with the external magnetic field.

In the first set of equations given in Wikipedia, the g-factor is defined as a positive value for the orbital and spin g-factors, while in the second set of equations, the g-factor is defined as a negative value for the orbital and spin g-factors. Both conventions are commonly used in literature, so it is important to clarify which convention is being used in your book.

In general, the g-factor for electrons, neutrons, and muons is negative because these particles have a negative charge, and the magnetic moment is defined in the opposite direction of the particle's spin. On the other hand, the g-factor for protons is positive because they have a positive charge and the magnetic moment is defined in the same direction as the particle's spin.

In conclusion, both sets of equations are correct, but they use different conventions for the sign of the g-factor. It is important to clarify which convention is being used in your book or in your research to avoid confusion.