GG 450 Magnetism February 7, 2008

QUIZ

Like gravity, magnetic fields are POTENTIAL fields, and we expect that we will be able to trade vectors for scalars at some point again. Unlike gravitational fields, we can easily generate large magnetic fields that overpower the earth's field, and we can effectively block out the earth's field if we want to.

Like gravity, magnetic fields are POTENTIAL fields, and we expect that we will be able to trade vectors for scalars at some point again. Unlike gravitational fields, we can easily generate large magnetic fields that overpower the earth's field, and we can effectively block out the earth's field if we want to.

Unlike gravitational fields, which always attract (as far as we know), magnetic fields generate both attractive and repulsive forces. Electrical and magnetic fields are impossible to separate, as one is created by the other. As far as we know, all magnetic fields are generated by moving electrical charge. Another way to think about it is that moving electrical charges exert "magnetic" forces on each other independent of the electrical forces.

What is a magnetic field? A magnetic field exists if a moving electric charge feels a non- electrostatic force at that point. (an electrostatic force is one that the charge would feel if it weren’t moving). A particle carrying an electrical charge passing through a magnetic field feels a force proportional to the amount of its charge and its velocity: where F is a vector force acting on the particle, H is the strength of the magnetic field, v is its velocity, q is its charge, and  is the angle between the magnetic field and the direction of motion of the particle.

DEFINITIONS: B: magnetic flux density, or magnetic induction, flux per unit area S.I. units are Tesla= 1 weber/m 2. A weber is a unit of magnetic pole strength. H: magnetic field strength (magnetic intensity), = B/  S.I. units: nanoTesla (nT) = gamma.  is the magnetic permeability, So, remember that H  B for small magnetic fields.

Right hand rule: If your right thumb is the direction of the electric current (+ charges), then the magnetic field is in the direction that your fingers point, and the force on the electrical charge is out from your palm. A charge moving in the direction of the magnetic field feels no magnetic force. Can you think of a common instrument in SOEST that makes direct use of this force? What direction does the charge feel the force in?

Which way is the particle above going to move? Is it accelerating?

Alternatively, if a wire is moved through a magnetic field, a current is generated in the wire. In this figure, the wire loop is forced to spin in the magnetic field. What happens when the wire loop continues half way around? What kind of device is this? What if we vary the magnetic field instead of forcing the wire to move?

What makes a material “magnetic”? Consider an electron revolving around the nucleus of an atom or around a molecule? The c urrent generated as the electron revolves is shown below as the arrowed circle, generating a magnetic field shown by the arrow: Indeed, this is the way many of the magnetic fields we are familiar with are formed. The strength of a magnet will depend on how many of these molecules are lined up in the same direction:

unmagnetized material - no external field weakly magnetized material Completely "saturated" ferromagnetic material - nearly all "domains" aligned. Very strong external field.

How do we quantify these fields? First: the force between two magnetic poles: where F = the force between the poles, m 1 and m 2 are the POLE STRENGTHs, r is the distance between the poles, and µ is called the MAGNETIC PERMEABILITY. This formula should look VERY familiar.

Every magnet has two poles - a plus and a minus, or N and S. Each pole generates a MAGNETIC FIELD whose strength is: H=m/r 2, where H is the magnetic field strength and m is the pole strength. H is what we measure in the field, and its units are nanoTesla or nT, (or gammas). In CGS units, one Oersted= 1 dyne/[unit pole strength] or 10 5 nT.

Permeability, μ, also called magnetic permeability, is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately x henry per meter (H/m) in free space (a vacuum). In other materials it can be much different, often substantially greater than the free-space value, which is symbolized µ o.

Materials that cause the lines of flux to move farther apart, resulting in a decrease in magnetic flux density compared with a vacuum, are called diamagnetic.

Materials that concentrate magnetic flux by a factor of more than 1 but less than or equal to 10 are called paramagnetic.

materials that concentrate the flux by a factor of more than 10 are called ferromagnetic. The permeability factors of some substances change with rising or falling temperature, or with the intensity of the applied magnetic field.

In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µo represents the permeability of free space (that is, x H/m) and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µ r, is given by: µ r = µ / µ o = µ (7.958 x 10 5 ) Diamagnetic materials have µ r less than 1, but no known substance has relative permeability much less than 1.

Magnetic moment is a measure of the torque generated by a pair of magnetic poles, called a magnetic couple: C=2 (m l) H sin  where C is a torque (force * distance) m is the pole strength and l is the distance between the poles. The magnetic moment is defined as M=ml. This torque causes a compass needle to turn to the north.

Magnetic intensity (I) is the moment per unit volume, or poles per unit area. As I increases, more of a body is magnetized and the field per unit area increases. Lines of Force: Lines of force external to a magnet go from + to -, or from the magnetic N pole to the S pole. Lines of force are perpendicular to surfaces of equal field strength. They are equivalent to “rays” in seismology and the direction of acceleration in gravity. They show the direction a magnetized body will feel a force in.

Magnetic susceptibility: When a material is placed in a magnetic field, some of its molecules flip to align with or against the "inducing" field. This generates another magnetic field called the induced field. The strength of the induced field relative to the inducing field for a given volume of material is a measure of its Magnetic susceptibility. I=kH, where I is the intensity of the induced field, k is the susceptibility, and H is the strength of the inducing field. Susceptibility is the fundamental parameter in magnetic prospecting.

Ferromagnetic materials - like iron - have very high susceptibilities. Diamagnetic materials - like quartz, have very small negative susceptibilities. paramagnetic materials - like pyroxene and olivine - have weak susceptibilities ferrimagnetic materials - like magnetite - have relatively high susceptibilities. Magnetite accounts for a large fraction of the susceptibility of rocks and for magnetic anomalies in the earth’s crust.

Induction of magnetic fields: Nearly all magnetic anomalies in shallow exploration are INDUCED. That is, they would go away if the earth's field went away. But some very important anomalies are REMANENT magnetizations - locked into the rock. These anomalies would NOT go away if the earth's field were switched off. Do you know any examples of remanent anomalies?

As we increase the strength of the inducing field H, more and more domains flip in response to this field, increasing the induced field I. As more and more magnetic domains are oriented the material becomes saturated, and the induce field reaches its highest possible value. This is called a hysteresis curve.

When the inducing field is removed, part of the induced field remains - termed the REMANENT magnetization. Some materials will hold a remanent magnetization when they cool from a melt (such as magnetite). This is the way that magnetic anomalies are generated on the seafloor.

As the ocean crust cools below about 700°C, the material passes through its CURIE POINT, where the magnetic field is locked in. If the rock is ever heated above the Curie point again, the remanent magnetic field will be lost, and when the rock cools again, the remanent field will change to the direction of the current field.

Another type of remanent magnetization can be caused by slow deposition of sediments. Laths of magnetite will tend to settle to the bottom pointing like little magnets with their north pole pointing north. This trend will magnetize the sediment depending on how much magnetic material is present.

Simple dipole magnetic fields: All magnets have two poles, a positive and negative pole. Lines of force go from the positive to the negative pole. A simple bar magnet showing lines of force. The closer the lines of force, the larger the magnetic field.

Two magnets with opposite poles near each other will be drawn together. When in contact, or close proximity, the two magnets will appear to be one large magnet.

Two magnets with the same pole towards each other will repel.