The Earth's magnetic field is essentially that of a magnetic dipole....

In summary, the Earth's magnetic field can be approximated as a dipole field, with a magnetic field near the North Pole of approximately 10^-4 T. Using the formula B = \frac{\mu _0}{2\pi}\frac{\mu}{x^3}, it can be determined that the magnetic field 13,000 km above the surface at the North Pole would be approximately the same as at the surface, assuming x >> R.
  • #1
hitemup
81
2

Homework Statement



The Earth's magnetic field is essentially that of a magnetic dipole. If the field near the North Pole is about 10^-4 T, what will it be (approximately) 13,000 km above the surface at the North Pole?

Homework Equations



[tex]B = \frac{\mu _0}{2\pi}\frac{\mu}{(R^2+x^2)^{3/2}}[/tex]

for x >> R

[tex]B = \frac{\mu _0}{2\pi}\frac{\mu}{x^3}[/tex]

The Attempt at a Solution



I know how to find the magnetic field of a dipole on its axis for a circle. My textbook uses the second formula to solve this problem. But I cannot understand what "x" and "R" are for the earth, and how we assumed x>>R.
 
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  • #2
Wherever you got that equation from (link?), it should state what the variables mean and what constraints there are on its validity. If you can't provide a link, please quote them.
The form of it (##R^2+x^2##), suggests R and x are orthogonal, which doesn't sound right for the given question.
 
  • #3
haruspex said:
Wherever you got that equation from (link?), it should state what the variables mean and what constraints there are on its validity. If you can't provide a link, please quote them.
The form of it (##R^2+x^2##), suggests R and x are orthogonal, which doesn't sound right for the given question.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c3

This is the same formula except pi*r^2*I is changed with mu(magnetic dipole moment) in mine.
 
  • #4
"Dipole field" is the name for the field from a current loop in the limit ##R\rightarrow 0##, with m or ##{\bf \mu} = \pi R^2 \;I## constant. So Haru is right and your book is right too.

That eliminates the R question. Now you should think about where this dipole could possibly be located, and therefore what to take for the x.
 

Related to The Earth's magnetic field is essentially that of a magnetic dipole....

1. What is a magnetic dipole?

A magnetic dipole is a type of magnet that has two poles, a north pole and a south pole, just like a bar magnet. However, unlike a bar magnet which is made of a solid material, a magnetic dipole is created by the movement of charged particles, such as electrons, within a material or a planet's core.

2. How is the Earth's magnetic field created?

The Earth's magnetic field is created by the movement of molten iron and nickel in its outer core. These charged particles create electric currents, which in turn generate a magnetic field. This process is known as the geodynamo.

3. Why is the Earth's magnetic field important?

The Earth's magnetic field plays a crucial role in protecting our planet from the harmful effects of the solar wind, a stream of charged particles emitted by the Sun. It also helps to guide migratory animals and aids in navigation for humans.

4. Does the Earth's magnetic field ever change?

Yes, the Earth's magnetic field is constantly changing, both in strength and direction. In fact, the magnetic poles have been known to reverse, where the north pole becomes the south pole and vice versa. This reversal occurs on average every 200,000 years.

5. How do scientists study the Earth's magnetic field?

Scientists use a variety of tools and techniques to study the Earth's magnetic field, including magnetometers, satellites, and geological records. They are also able to simulate the Earth's magnetic field in laboratories to better understand its behavior and changes over time.

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