Geophysics Lec11

8/13/2019 Geophysics Lec11

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Geomagnetism: Lecture 1

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

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The Coulomb (magnetic) force: the definition

According to the Coulomb law , the magnetic force , F m, actingbetween two magnetic monopoles is given by:

where:

is a constant of proportionality known as the magneticpermeability .

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

r is the distance between the two poles.

F m 1

p1 p2r 2

,


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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].

In other words, if the force is equal 1 Newton and the twomagnetic poles are separated by 1 meter, the poles charge isequal to 1 Ampere meter.


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Note the similarities to the gravitational force, i.e., the 1/r 2 dependence.

Unlike the gravitational constant, the magnetic permeability, , isa material property.

p 1 and p 2 can be either of a positive or a negative sign. If p 1 andp2 are of the same sign, the Coulomb force is repulsive, otherwise

it is attractive.

The Coulomb (magnetic) force: related notes


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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), andcompute the magnetic force.3. Repeat step-2 by moving the positive pole to a new location.

The Coulomb (magnetic) force: magnetic monopoles


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Similarly, one can get a positive monopole:



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

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



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A common way to visualize the magnetic force field associatedwith a magnetic dipole is to plot the field lines for the force. Fieldlines are a set of lines drawn such that they are everywhereparallel to the direction of the force.

The Coulomb (magnetic) force: field lines


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A comment on Brunton compass adjustment...

The geomagnetic field

geomagnetic field = dipole + nondipole.


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

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


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Two main effects act to produce a nondipole field:

1) Solar wind.



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2) Screening by the mantle and the lithosphere.



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The strength of the geomagnetic field

The magnetic field strength , H, is defined as the force per unitpole exerted by a magnetic monopole, p 1:

H F m p2

1

p1r 2

.

Note that the magnetic field strength is the magnetic analog tothe 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 ismore common to use units of nanoTeslas , nT. The averagestrength of the Earth's magnetic field is about 50,000 nT.


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

While the gravitational field maybe described as a sum of monopoles(single point sources), 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 withtime, the magnetic field is highly time dependent.

Differences between geomagnetics and gravity


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

While the spatial variation indensity are relatively small (between

1 and 3 Kg m -3 , magneticsusceptibility can vary as much asfour to five orders of magnitude.

Wide variations in susceptibilityoccur within a given rock type. Thus,it will be extremely difficult todetermine rock types based onmagnetic prospecting

Induced magnetization and magnetic susceptibility


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Induced magnetization and magnetic susceptibility

The value of the magnetic susceptibility can take on either positive

or negative values.

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


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Remnant magnetization

If the magnetic material has relatively large susceptibilities , or ifthe inducing field is strong, the magnetic material will retain aportion of its induced magnetization even after the induced fielddisappears. This remaining magnetization is called remnantmagnetization .

The total magnetic field is a sumof the main magnetic field

produced in the Earth's core, andthe remnant field within thematerial.

remnant

induced

total

b h f ld


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Describing the magnetic field at a point

Declination : The angle between north and the horizontal

projection of the magnetic vector. This value is measured positivethrough east and varies from 0 to 360 degrees.

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

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