Geomagnetism: Lecture 1

This lecture is based largely on: http://www.earthsci.unimelb.edu.au/ES304/

The Coulomb (magnetic) force: the definition

According to the Coulomb law, the magnetic force, Fm, acting between two magnetic monopoles is given by:

where:

• is a constant of proportionality known as the magnetic permeability.

• p1 and p2 are the charges of the two magnetic monopoles.

• r is the distance between the two poles.

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Fm =1

μ

p1p2

r2,

The Coulomb (magnetic) force: the units

The units in SI are:

• Fn is in Newtons [N].

• r is in meters [m].

• p1 and p2 are in Ampere times meter [Amp m].

• is a unitless constant.

€

Fm =1

μ

p1p2

r2,

• Note the similarities to the gravitational force, i.e., the 1/r2 dependence.

• Unlike the gravitational constant, the magnetic permeability, , is a material property.

• p1 and p2 can be either of a positive or a negative sign. If p1 and p2 are of the same sign, the Coulomb force is repulsive, otherwise it is attractive.

The Coulomb (magnetic) force: related notes

A recipe for calculating a magnetic monopole:

1. Place a negative pole at (-1,0).2. Take a positive pole and place it at some location (x,z), and compute the magnetic force.3. Repeat step-2 by moving the positive pole to a new location.

The Coulomb (magnetic) force: magnetic monopoles

Similarly, one can get a negative monopole:

The Coulomb (magnetic) force: magnetic monopoles

Magnetic monopoles have never actually been observed! Instead, the fundamental magnetic element is the magnetic dipole, which consists of two magnetic monopoles.

The dipole is obtained by vector addition of a negative and a positive monopole.

Note that the arrows come out of the monopole labeled N and into the monopole labeled S.

The Coulomb (magnetic) force: magnetic monopoles

A common way to visualize the magnetic force field associated with a magnetic dipole is to plot the field lines for the force. Field lines are a set of lines drawn such that they are everywhere parallel to the direction of the force.

The Coulomb (magnetic) force: field lines

• A comment on Brunton compass adjustment...

The geomagnetic field

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geomagnetic field = dipole + nondipole.

The origin of the dipole field is in the liquid core. This field and its reversals have been simulated numerically by Glazmaire and Roberts [1995].

http://www.psc.edu/research/graphics/gallery/geodynamo.html

The geomagnetic field

“The following images and animations show views of a snapshot from a 3D time dependent computer simulation of convection and magnetic field generation in the Earth's liquid core that spans over 80,000 years. The simulation took several thousand cpu hours on the Cray C-90. Magnetic field lines show the direction and intensity of the generated magnetic field. Lines are colored gold where the field is directed outward and blue where it is directed inward.” (Gary Glatzmaier, Los Alamos and Paul Roberts, UCLA)

http://www.psc.edu/research/graphics/gallery/geodynamo.html

The geomagnetic field

The reversal - Earth The reversal + Earth

Nondipole field:

Question: what gives rise to the nondipole component?

The geomagnetic field

Two main effects act to produce a nondipole field:

1) Solar wind.

The geomagnetic field

2) Screening by the mantle and the lithosphere.

The geomagnetic field

The strength of the geomagnetic field

The magnetic field strength, H, is defined as the force per unit pole exerted by a magnetic monopole, p1:

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H =Fmp2

=1

μ

p1

r2.

• Note that the magnetic field strength is the magnetic analog to the gravitational acceleration.

• H is measured in units of Tesla ,T, where: 1 T = N Amp-1 m-1.

• When describing the magnetic field strength of the earth, it is more common to use units of nanoTeslas, nT. The average strength of the Earth's magnetic field is about 50,000 nT.

Similarities between geomagnetics and gravity

• Passive measurement of a naturally occurring field of the earth.

• Potential fields - thus, the mathematics is similar.

• The interpretations are non-unique.

• While the gravitational force is always attractive, the magnetic force can be either attractive or repulsive.

• While the gravitational field is amonopole (single point source), thegeomagnetic field is described interms of magnetic dipole, i.e., thesum of a positive and a negativemonopole.

• While the gravitational field does not change significantly with time, the magnetic field is highly time dependent.

Differences between geomagnetics and gravity

Induced magnetization and magnetic susceptibility

When a magnetic material is placed within a magnetic field, H, the magnetic material will produce its own magnetization.

The intensity of the induced magnetization, Ji, is given by:

where , the magnetic susceptibility, is a unitless number, property of the material.

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Ji = χH,

• The values given here are for SI, International System Units.

• While the spatial variation in density are relatively small (between 1 and 3 Kg m-3, magnetic susceptibility can vary as much as four to five orders of magnitude.

• Wide variations in susceptibility occur within a given rock type. Thus, it will be extremely difficult to determine rock types based on magnetic prospecting

Induced magnetization and magnetic susceptibility

Induced magnetization and magnetic susceptibility

The value of the magnetic susceptibility can take on either positive or negative signs.

Positive value means that the induced magnetic field, I, is in the same direction as the inducing field, H.

Induced magnetization and magnetic susceptibility

Negative value means that the induced magnetic field is in the opposite direction as the inducing field.

Remnant magnetization

If the magnetic material has relatively large susceptibilities, or if the inducing field is strong, the magnetic material will retain a portion of its induced magnetization even after the induced field disappears. This remaining magnetization is called remnantmagnetization.

The total magnetic field is a sumof the main magnetic fieldproduced in the Earth's core, andthe remnant field within thematerial.

remnantinduced

total

Describing the magnetic field at a point

• Declination: The angle between north and the horizontal projection of the magnetic vector. This value is measured positive through east and varies from 0 to 360 degrees.

• Inclination: The angle between the surface of the earth and the magnetic vector. Positive declinations indicate the vector points downward, negative declinations indicate it points upward. Declination varies between -90 and 90 degrees.