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Systems of Units
APPENDIX A
Systems of Units
See [B.81, Chapter 1]. All the relations between magnetic quantifies given in this book are expressed in the SI system of units. In this system, the relation holds,
B-/z0(H + M)
(A.1)
/1o = 4r 10 -7 [H m -1]
(A.2)
where
measured in units of henry per meter [H m -1], is the permeability of the vacuum. The magnetization M and the magnetic field H are measured in units of amp&e per meter [A m-l]. The magnetic polarization I = A M (the symbol J is also employed instead of I) is often used as an alternative to M. Writing Eq. (A.1) as B = ]z0H + I amounts to adopting the so-called Kennelly convention. Equation (A.1) expresses instead the Sommerfeld convention. I, like B, is measured in units of weber per square meter [Wb m-2], also called tesla [T]. For simplicity, the same term, "magnetization," is employed to refer to M as well as to I, depending on convenience. Many of the results in the literature are still expressed in the Gaussian c.g.s, system of units. In this system, Eq. (A.1) is written in the form B = H + 4r
(A.3)
B, H, M thus have all the same dimensions. In spite of this, different names are used for the units in which the various fields are measured. The magnetic field H is measured in units of oersted [Oe], the magnetic induction B is measured in gauss [G], and the magnetization M is measured in emu per cube centimeter [emu cm-3]. Notice that there are many cases where the quantity 4caM, expressed in [G] units, is considered in place 509
510
APPENDIX A
Systems of Units
of M. The conversion factors from one system to the other are given in Table A.1. TABLE A.1
Quantity
B
Conversion factors for systems of units SI Unit
Gaussian Unit
weber per square meter [Wb m -2] o r tesla [T] l I W b m -2]
=
Conversion Factor
gauss [G]
1 [G] = 10 -4 [T]
I[T]
H
amp6re per meter [ A m -1]
oersted [Oe]
1 [Oe] = 103/4"a" [ A m -1] -~ 79.6 [A m -11
M
amp6re per meter [ A m -1]
emu per cube centimeter [emu cm -3]
1 [emu cm -3] = 10 3 [A m -1]
~oM, 4"rrM
weber per square meter [Wb m -2] o r tesla [T] 1 [Wb m -2] = 1 [T]
gauss [G]
1 [G] = 10 -4 [W]
Systems of Units
See [B.81, Chapter 1]. All the relations between magnetic quantifies given in this book are expressed in the SI system of units. In this system, the relation holds,
B-/z0(H + M)
(A.1)
/1o = 4r 10 -7 [H m -1]
(A.2)
where
measured in units of henry per meter [H m -1], is the permeability of the vacuum. The magnetization M and the magnetic field H are measured in units of amp&e per meter [A m-l]. The magnetic polarization I = A M (the symbol J is also employed instead of I) is often used as an alternative to M. Writing Eq. (A.1) as B = ]z0H + I amounts to adopting the so-called Kennelly convention. Equation (A.1) expresses instead the Sommerfeld convention. I, like B, is measured in units of weber per square meter [Wb m-2], also called tesla [T]. For simplicity, the same term, "magnetization," is employed to refer to M as well as to I, depending on convenience. Many of the results in the literature are still expressed in the Gaussian c.g.s, system of units. In this system, Eq. (A.1) is written in the form B = H + 4r
(A.3)
B, H, M thus have all the same dimensions. In spite of this, different names are used for the units in which the various fields are measured. The magnetic field H is measured in units of oersted [Oe], the magnetic induction B is measured in gauss [G], and the magnetization M is measured in emu per cube centimeter [emu cm-3]. Notice that there are many cases where the quantity 4caM, expressed in [G] units, is considered in place 509
510
APPENDIX A
Systems of Units
of M. The conversion factors from one system to the other are given in Table A.1. TABLE A.1
Quantity
B
Conversion factors for systems of units SI Unit
Gaussian Unit
weber per square meter [Wb m -2] o r tesla [T] l I W b m -2]
=
Conversion Factor
gauss [G]
1 [G] = 10 -4 [T]
I[T]
H
amp6re per meter [ A m -1]
oersted [Oe]
1 [Oe] = 103/4"a" [ A m -1] -~ 79.6 [A m -11
M
amp6re per meter [ A m -1]
emu per cube centimeter [emu cm -3]
1 [emu cm -3] = 10 3 [A m -1]
~oM, 4"rrM
weber per square meter [Wb m -2] o r tesla [T] 1 [Wb m -2] = 1 [T]
gauss [G]
1 [G] = 10 -4 [W]