Bar Magnet

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

Contents [hide] 
1 The Main Idea
1.1 A Mathematical Model
1.2 A Computational Model
2 Examples
2.1 Simple
2.2 Middling
2.3 Difficult
3 Connectedness
4 History
5 See also
5.1 Further reading
5.2 External links
6 References

== The Main Idea == [edit]

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The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

A Mathematical Model[edit]

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Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that: [math]\displaystyle{ B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}} }[/math]

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we conclude that: [math]\displaystyle{ B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}} }[/math]

A Computational Model[edit]

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As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees! It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

Examples[edit]

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Example 1: If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

Example 2: A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

(a) Which end of the bar magnet is closest to the compass? (b) How many turns of wire are in the coil?

Part A Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the NORTH end would have to be nearest the compass (because the field flows out of the north end into the positive end).

Simple[edit] Middling[edit] Difficult[edit] Connectedness[edit] How is this topic connected to something that you are interested in? How is it connected to your major? Is there an interesting industrial application? History[edit] Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also[edit] Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading[edit] Books, Articles or other print media on this topic

External links[edit] [1]

References[edit] This section contains the the references you used while writing this page

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