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[[Image:l shell global dipole.png|thumb|Plot showing field lines (which, in three dimensions would describe "shells") for [[L-shell|L-values]] 1.5, 2, 3, 4 and 5 using a dipole model of the Earth's magnetic field]]


The '''dipole model of the Earth's magnetic field''' is a first order approximation of the rather complex true [[Earth's magnetic field]].  Due to effects of the [[interplanetary magnetic field]], and the [[solar wind]], the dipole model is particularly inaccurate at high [[L-shell]]s (e.g., above L=3), but may be a good approximation for lower L-shells.  For more precise work, or for any work at higher L-shells, a more accurate model that incorporates solar effects, such as the [[Tsyganenko magnetic field model]], is recommended.


==Equations==
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The following equations describe the dipole magnetic field.<ref name="walt">{{cite book |last= Walt |first= Martin |title= [[Introduction to Geomagnetically Trapped Radiation]] |pages = 29–33 |publisher= [[Cambridge University Press]] |location = New York, NY |year= 1994 |isbn= 0-521-61611-5}}</ref>
 
First, define <math>B_0</math> as the mean value of the magnetic field at the magnetic equator on the Earth's surface.   Typically <math>B_0=3.12\times10^{-5}\ \textrm{T}</math>.
 
Then, the radial and azimuthal fields can be described as
 
<math>B_r = -2B_0\left(\frac{R_E}{r}\right)^3\cos\theta</math>
 
<math>B_\theta = -B_0\left(\frac{R_E}{r}\right)^3\sin\theta</math>
 
<math>|B| = B_0\left(\frac{R_E}{r}\right)^3 \sqrt{1 + 3\cos^2\theta}</math>
 
where <math>R_E</math> is the mean [[Earth radius|radius of the Earth]] (approximately 6370&nbsp;km), <math>r</math> is the radial distance from the center of the Earth (using the same units as used for <math>R_E</math>), and <math>\theta</math> is the azimuth measured from the north magnetic pole.
 
It is sometimes more convenient to express the magnetic field in terms of magnetic latitude and distance in earth radii. The magnetic latitude <math>\lambda</math> is measured northwards from the equator (analogous to [[latitude|geographic latitude]]) and is related to <math>\theta</math> by <math>\lambda = \pi/2 - \theta</math>. In this case, the radial and azimuthal components of the magnetic field (the latter still in the <math>\theta</math> direction, measured from the axis of the north pole) are given by
 
<math>B_r = -\frac{2B_0}{R^3}\sin\lambda</math>
 
<math>B_\theta = \frac{B_0}{R^3}\cos\lambda</math>
 
<math>|B| = \frac{B_0}{R^3} \sqrt{1 + 3\sin^2\lambda}</math>
 
where <math>R</math> in this case has units of Earth radii (<math>R = r/R_E</math>).
 
==Invariant latitude==
Invariant latitude is a parameter that describes where a particular magnetic field line touches the surface of the Earth. It is given by<ref name="Kivelson-Russell">{{cite book |last1= Kivelson |first1= Margaret |last2= Russell |first2= Christopher |title= [[Introduction to Space Physics]] |pages = 166–167 |publisher= [[Cambridge University Press]] |location = New York, NY |year= 1995 |isbn= 0-521-45714-9}}</ref>
 
<math>\Lambda = \arccos\left(\sqrt{1/L}\right)</math>
 
or
 
<math>L = 1/\cos^2\left(\Lambda\right)</math>
 
where <math>\Lambda</math> is the invariant latitude and <math>L</math> is the L-shell describing the magnetic field line in question.
 
On the surface of the earth, the invariant latitude (<math>\Lambda</math>) is equal to the magnetic latitude (<math>\lambda</math>).
 
==See also==
*[[Earth's magnetic field]]
*[[Dipole]]
*[[L-shell]]
 
==References==
{{reflist}}
 
==External links==
*[http://ccmc.gsfc.nasa.gov/models/modelinfo.php?model=Tsyganenko%20Model Instant run of Tsyganenko magnetic field model] from NASA CCMC
*[http://geo.phys.spbu.ru/~tsyganenko/modeling.html Nikolai Tsyganenko's website] including Tsyganenko model source code
 
{{DEFAULTSORT:Dipole Model Of The Earth's Magnetic Field}}
[[Category:Geomagnetism]]
[[Category:Space physics]]

Latest revision as of 08:50, 10 April 2014


They have powerful and durable mountain bikes with a high-tech suspension system. Mountain biking accessories come in all different forms and you do not need all of them. As a result of this various protective gear manufacturers have also ventured into production of improved design of padded shorts. Riding position is typically more vertical than that of a road bike. Certain Haro mountain bike models worth mentioning right here consist of BMX Black trail X1, BMX Haro Partial 16, BMX Haro FIC and so forth.

You can choose from many different suspensions on your bike, make sure the suspension you choose is going to fit the type of cycling you intend for it. In case you have just about any inquiries regarding in which and also how you can work with Biking for modern life mountain bike sizing., you'll be able to contact us on our site. Now most people wear gloves whilst they are riding because they keep the hands warm. From free shipping on all the bikes across the US, the Road Bike Outlet makes consumers happy anywhere within 1 to 6 days. From personal experience they can be not easy to maintain by yourself so a mechanical system may be better for you. A smart shopper knows his or her rights, and you should also know this before finalizing any purchase or transaction online.

Mountain bikes in Arizona have two great rides in Sedona, Highline and the Dry Creek Loop. Mulberry Gap Mountain Bike Get-A-Way is located 12 miles from downtown Ellijay in the Chattahoochee National Forest with some of the best single track mountain bike trails including the Georgia Pinhoti trail system. Please remember the stem lengths can impact just how reactive the bike is. The Grand Rapids area is becoming well known as a cycling destination. One of the obvious things to check on both a bike and car are brakes.

The inaugural Big Bear Gran Fondo takes place on July 26th in Big Bear, with distance options of 20K, 30K, 70K and 100K. This article discusses how to go about buying a mountain bike. It is primarily design of Billet Motorola clutch kit that replaces your stock clutch within your GPX 150, 160 and additionally YX 140, 150, 160. The dedication and solid experience of the experts, it is not difficult to accomplish such goal. I've never been into cycling and wanted to give it a try for exercise.

In the recent article section, you can find the list of biking related articles with a detailed description present on the official website. The bike should be examined to check it is working correctly. Trying out various sizes is the first step in choosing the correct folding bike. Whether it's a testament to South Dakota's commitment to recycling, or just whimsy, Bone Collector embodies the features of the best bike trails in the world: Sedona, Moab, Flagstaff, Whistler and Tahoe, without the long drive or expensive plane ticket. Part of Park City's distinction as the International Mountain Bike Association's first and only gold-level Ride Center is its abundance of beginner trails.

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