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Collection: Alexa Crawls

Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period.

TIMESTAMPS

Read Suggestions for the Use of SI Units in Magnetism
Fundamental Units (From Resnick and Halliday, Physics, Part I, 1968, Wiley)

Coulomb's Law

• a force exists between 2 magnetic poles:
  
• where
  is the force
  is the permeability of free space, =
  , are the magnetic pole strength
  is the distance separating the poles
  is the unit radial vector
   
• unlike gravity, poles come in 2 flavors:
  • + (north-seeking)
  • - (south-seeking)
  • like poles repel (F is +, force is outward)
  • unlike poles attract (F is -, force is inward)

  Magnetic Induction, B

  • as with gravity, we are interested in force Earth exerts on a unit pole (like acceleration, with g)
  • or, 'magnetic field intensity'
  • analogous to gravitational acceleration (but not acceleration units!)
  • force per unit pole strength (force exerted on unit magnetic pole)

  

  (In our analogy with gravity, m here is the Earth's "monopole" field, which is a fiction; Stacey incorrectly calls B "magnetic field, which is H)

  Magnetic Field Strength, H

  • if we only had to deal with a vacuum (or even air, since it has negligible magnetic susceptibility), we could always deal with H (magnetic field strength)..
  • however, in presence of "magnetizable" material, there is a magnetic polarization (or, simply, magnetization) of material which produces an additional field (J) which adds to H
  • combining the field strength, H, and the magnetic polarization (magnetization), J, is call the magnetic induction, B

  cgs system

  • magnetic induction, B, is related to magnetic field, H, by

  B = H + 4pJ (note that B, H, J, [and M, below]  have the same units)

  • J, magnetic polarization (or magnetization) and M, the magnetic dipole moment per unit volume are related by

  J = M

  SI system

  B = m₀H + J

  J = m₀M

  where m₀ = 4p x 10^-7 H/m (Henry/meter) is the permeability of free space

  Units

  cgs system

  • from above, all four fundamental terms have the same units in cgs system, but is has been customary to use:

  B	magnetic induction	gauss	G
  H	magnetic field	oersted	Oe
  J	magnetic polarization, magnetization	electromagnetic units	emu
  M	magnetic dipole moment per unit volume	electromagnetic units	emu

  SI system

  • in SI, for force of 1 Newton and 1 unit pole strength: A/m (H), or Tesla (B)

  B	magnetic induction	tesla	T
  H	magnetic field	amperes per meter	A/m
  J	magnetic polarization, magnetization	tesla	T
  M	magnetic dipole moment per unit volume	amperes per meter	A/m

  • since these units are very large quantities, for exploration work:
    • 1 A/m (H), or Tesla (B) = 10⁹ nanotesla (nT)
    • 1 Oersted (Oe) = 10⁵ g (gamma)
    • 1 g equivalent to nT

Definition of magnetic permeability

Magnetic Potential

• Since H or B are central force fields (depend only on r), they are conservative, and can be represented as gradient of a scalar, potential field.  And since the field are proportional to 1/r², they obey LaPlace's equation. The scalar potential is
  
  and
  
  when there is no magnetic material is present,
  
  where H is the magnetic field strength, else,
  where is relative magnetic permeability.

Magnetic Dipole

• In nature we find dipoles, not monopoles
• A dipole consists of two poles of opposite polarity and equal strength.

  Have physicists seen magnetic monopoles?
   

• The strength of a dipole depends on strength of magnetization of poles and their separation, and is a vector quantity known as dipole moment, which is analogous to mass in gravity:
  
  M = ml
  
  where M is a vector directed from the negative pole to the positive pole
• The dipole moment is analogous to mass
• As we shall see, though, unlike mass, for which potential drops off like 1/r, the potential field of a dipole drops off like 1/r²  (field drops off like?)

Intensity of magnetization

Magnetic dipole moment is an extensive quantity (like mass). In analogy with gravity, magnetic dipole moment per unit volume is  an intensive quantity (like density). This is also called the intensity of magnetization, or

I = M/volume = ml/volume = m/area

where I and M are vector quantities.

Potential due to a Dipole

The potential due to a dipole is found by summing the potentials of the individual poles:

• 
• so the total potential is (after bringing outside),
  
• the basic dipole consists of spinning electron (current loop), where l and hence l/r are small, so we neglect terms of (l/r)²,  and use Taylor's series:
  
  
  eliminating terms, we get
  

Field of Magnetic Dipole

Fig. 4.8. Magnetic field of a dipole. Dipole m is oriented toward top of page. Vectors indicate the direction of B that would be observed at the center of each vector. Dashed contours indicate constant values of |B|, the value decreasing by a factor of 10 at each succeeding contour from the dipole; that is, if the closest contour to the dipole has the value |B| = 1, succeeding contours have the values 0.1, 0.01, and 0.001, respectively.

Quotes

• obtain vector field by taking gradient of potential, and find the components of this vector field:
  
  
  
• in MKS, the magnetic induction components are
• N.B.
  • B (and H) depend on 1/r³
  • for given r, field is greatest on axis with dipole
  • B_q = 0 at magnetic "pole"
  • B_r = 0 at magnetic "equator"
  • sign convention: Positive pole attracted toward Earth's N pole (north-seeking pole)