However, before magnetization these regions are small and randomly oriented throughout the unmagnetized ferromagnetic objects, so there is no net magnetic field. In response to an external magnetic field like the one applied in the above figure, these regions grow and become aligned. This arrangement can become permanent when the ferromagnetic material is heated and then cooled. Making a Ferromagnet : An unmagnetized piece of iron is placed between two magnets, heated, and then cooled, or simply tapped when cold.
The iron becomes a permanent magnet with the poles aligned as shown: its south pole is adjacent to the north pole of the original magnet, and its north pole is adjacent to the south pole of the original magnet. Note that there are attractive forces between the magnets. Magnetic field lines are useful for visually representing the strength and direction of the magnetic field.
Einstein is said to have been fascinated by a compass as a child, perhaps musing on how the needle felt a force without direct physical contact. His ability to think deeply and clearly about action at a distance, particularly for gravitational, electric, and magnetic forces, later enabled him to create his revolutionary theory of relativity.
Since magnetic forces act at a distance, we define a magnetic field to represent magnetic forces. A pictorial representation of magnetic field lines is very useful in visualizing the strength and direction of the magnetic field.
The direction of magnetic field lines is defined to be the direction in which the north end of a compass needle points. The magnetic field is traditionally called the B-field. Visualizing Magnetic Field Lines : Magnetic field lines are defined to have the direction that a small compass points when placed at a location. B Connecting the arrows gives continuous magnetic field lines.
The strength of the field is proportional to the closeness or density of the lines. C If the interior of the magnet could be probed, the field lines would be found to form continuous closed loops. Mapping the magnetic field of an object is simple in principle. First, measure the strength and direction of the magnetic field at a large number of locations or at every point in space.
Then, mark each location with an arrow called a vector pointing in the direction of the local magnetic field with its magnitude proportional to the strength of the magnetic field producing a vector field.
The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and the local density of field lines can be made proportional to its strength. Magnetic field lines are like the contour lines constant altitude on a topographic map in that they represent something continuous, and a different mapping scale would show more or fewer lines. These concepts can be quickly translated to their mathematical form. For example, the number of field lines through a given surface is the surface integral of the magnetic field.
Bar Magnet and Magnetic Field Lines : The direction of magnetic field lines represented by the alignment of iron filings sprinkled on paper placed above a bar magnet. Small compasses used to test a magnetic field will not disturb it. This is analogous to the way we tested electric fields with a small test charge. In both cases, the fields represent only the object creating them and not the probe testing them.
Figure shows how the magnetic field appears for a current loop and a long straight wire, as could be explored with small compasses. A small compass placed in these fields will align itself parallel to the field line at its location, with its north pole pointing in the direction of B. Note the symbols used for field into and out of the paper. Mapping Magnetic Field Lines : Small compasses could be used to map the fields shown here. A The magnetic field of a circular current loop is similar to that of a bar magnet.
B A long and straight wire creates a field with magnetic field lines forming circular loops. C When the wire is in the plane of the paper, the field is perpendicular to the paper. Note that the symbols used for the field pointing inward like the tail of an arrow and the field pointing outward like the tip of an arrow. Extensive exploration of magnetic fields has revealed a number of hard-and-fast rules. We use magnetic field lines to represent the field the lines are a pictorial tool, not a physical entity in and of themselves.
The properties of magnetic field lines can be summarized by these rules:. The last property is related to the fact that the north and south poles cannot be separated. It is a distinct difference from electric field lines, which begin and end on the positive and negative charges.
If magnetic monopoles existed, then magnetic field lines would begin and end on them. Earth is largely protected from the solar wind, a stream of energetic charged particles emanating from the sun, by its magnetic field, which deflects most of the charged particles.
These particles would strip away the ozone layer, which protects Earth from harmful ultraviolet rays. The region above the ionosphere, and extending several tens of thousands of kilometers into space, is called the magnetosphere.
This region protects Earth from cosmic rays that would strip away the upper atmosphere, including the ozone layer that protects our planet from harmful ultraviolet radiation.
The magnetic field strength ranges from approximately 25 to 65 microteslas 0. The intensity of the field is greatest near the poles and weaker near the equator. These effects can be combined into a partial differential equation called the magnetic induction equation:. It turns out that the closer you get to the wire, the stronger the magnetic field, and the further you get out, the weaker the magnetic field. And that kind of makes sense if you imagine the magnetic field spreading out.
I don't want to go into too sophisticated analogies. But if you imagine the magnetic field spreading out, and as it goes further and further out it kind of gets distributed over a wider and wider circumference. And actually the formula I'm going to give you kind of has a taste for that. So the formula for the magnetic field-- and it really is defined with a cross product and things like that, but for our purposes we won't worry about that.
You'll just have to know that this is the shape if the current is going in that direction. And, of course, if the current was going downwards then the magnetic field would just reverse directions. But it would still be in co-centric circles around the wire. But anyway, what is the magnitude of that field? The magnitude of that magnetic field is equal to mu-- which is a Greek letter, which I will explain in a second-- times the current divided by 2 pi r.
So this has a little bit of a feel for what I was saying before. That the further you go out-- where r is how far you are from the wire-- the further you go out, if r gets bigger, the magnitude of the magnetic field is going to get weaker.
And this 2 pi r, that looks a lot like the circumference of a circle. So that gives you a taste for it. I know I haven't proved anything rigorously. But it at least gives you a sense of, look there's a little formula for circumference of a circle here. And that kind of makes sense, right? Because the magnetic field at that point is kind of a circle. The magnitude is equal at an equal radius around that wire. Now what is this mu, this thing that looks like a u? Well, that's the permeability of the material that the wire's in.
So the magnetic field is actually going to have a different strength depending on whether this wire is going through rubber, whether it's going through a vacuum, or air, or metal, or water. And for the purposes of your high school physics class, we assume that it's going through air normally. And the value for air is pretty close to the value for a vacuum. And it's called the permeability of a vacuum. And I forget what that value is.
I could look it up. But it actually turns out that your calculator has that value. So let's do a problem, just to put some numbers to the formula. So let's say I had this current and it is-- I don't know, the current is equal to-- I'm going to make up a number.
And let's say that I just pick a point right here that is-- let's say that that's 3 meters away from the wire in question. So my question to you is what is the magnitude in the direction of the magnetic field right there? Well, the magnitude is easy. We just substitute in this equation. So the magnitude of the magnetic field at this point is equal to-- and we assume that the wire's going through air or a vacuum-- the permeability of free space-- that's just a constant, though it looks fancy-- times the current times 2 amperes divided by 2 pi r.
What's r? It's 3 meters. So 2 pi times 3. So it equals the permeability of free space. So let's see. The 2 and the 2 cancel out over 3 pi. So how do we calculate that? Well, we get out our trusty TI calculator. And I think you'll be maybe pleasantly surprised or shocked to realize that-- I deleted everything just so you can see how I get there-- that it actually has the permeability of free space stored in it. So what you do is you go to second and you press constant, which is the 4 button. It's in the built-in constants.
Even in Maxwell's equations, there are terms connecting magnetic and electric fields, so that propagating field waves always contained both, not just one or the other. In special relativity, going from one reference frame to another changes the fields from one type to another.
In other words, if you have an electric field but no magnetic field in some frame, if you look in a relatively moving frame there will be a different electric field and now some magnetic field.
Likewise if you have a magnetic field but no electrc field in some frame, if you look in a relatively moving frame there will be a different magnetic field and now some electric field. Follow-up on this answer. Learn more physics! Related Questions.
Still Curious? Why does a solenoid behave like a bar magnet? I'd like to reverse the question: why does a bar magnet behave like a solenoid? Mike W. How are electricity and magnetism unified under electromagnetism? Why are they considered a single force? I've marked this as a follow-up to a related question.
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