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Magnetic Fields
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About the lecture
In this mini-lecture, we introduce the concept of magnetic fields. In particular. We consider: (i) natural magnets, where we see that like poles repel while opposite poles attract; (ii) magnetic field lines, which are always closed and describe the magnetic field strength depending on the density of lines; (iii) the magnetic field of an infinite wire carrying current; and (iv) the magnetic field lines of other current-carrying wires, such as a loop.
About the lecturer
Mohamed Anber is a Professor of Mathematical and Theoretical Particle Physics at Durham University. At the time of filming his course on magnetism, he was a Professor of Physics at Lewis & Clark College in Portland, Oregon in the United States. His research interests involve a broad range of theoretical physics topics, including those in quantum field theory and theoretical cosmology.
Hello.
00:00:06I am Mohammed Amber,
00:00:06professor in the physics department at Lewis and Clark College.
00:00:08So let us start with the concept of the magnetic field.
00:00:13So we all know
00:00:20about the natural magnets.
00:00:22So if you have a natural magnet, which is basically a piece of iron,
00:00:24you will discover that the magnet consists of two polls.
00:00:31It has called them the North Pole and the South Pole. Now let us bring another magnet.
00:00:36So also the other magnet will have two polls.
00:00:45This is the North Pole, and this is the South Pole,
00:00:49north and south. Now you can ask yourself the question.
00:00:56What happens if you try to bring the north Pole's close to each other?
00:01:00So if you try to bring the north Pole's close to each other,
00:01:07you will find that the two magnets repel each other,
00:01:11and the same thing happens if you try to bring the south polls close to each other.
00:01:18You will also find that the magnets repel.
00:01:23However, let us try to, uh, do the converse. Okay. Again, we have two magnets
00:01:26north and south.
00:01:36But now let us take the second magnets.
00:01:44Touch that we bring the south close to the north
00:01:47and the north, close to the south.
00:01:52And now you will find that the magnets attract.
00:01:55So we attribute that to the existence of a magnetic force.
00:01:59But what we see now that like polls
00:02:04and the bill
00:02:13and unlike pulse
00:02:17attract
00:02:23due to this magnetic force,
00:02:25instead of working with the magnetic force directly,
00:02:28we introduced a concept called the Field the magnetic field.
00:02:32And this is a physical as well as a mathematical concept that will enable us to, um,
00:02:37analyse the magnetism, magnetism, um, in great details.
00:02:44So it turns out that, uh, there is a magnetic field. So again, this is our magnet.
00:02:50It may just draw it first,
00:02:59and you can think OK of a magnetic field.
00:03:05So this magnetic field is a vector field,
00:03:11and it can be drawn as closed lines that start from
00:03:16the North Pole and go back to the South Pole.
00:03:21Something like that
00:03:25again.
00:03:28Okay,
00:03:29so there are magnetic field lines started from the North Pole and
00:03:29the claws on themselves when you go back to the South Pole,
00:03:35etcetera.
00:03:39So we have something like that.
00:03:46So these are called the field. The magnetic field lines
00:03:49and as you can see, that they are always closed lines.
00:03:56Of course,
00:04:02the density of these field lines will depend
00:04:05on the strength of the magnetic field itself.
00:04:08This has always to be true.
00:04:17Now you might ask
00:04:24how you can connect the concept of the magnetic field to the magnetic force.
00:04:26The thing that you really experience in the lab, I will come to that later.
00:04:30But before that, let me also tell you that in order to generate the magnetic field,
00:04:35you don't have to have only natural magnets.
00:04:41You can actually generate the magnetic field by letting
00:04:44a current an electric current bus through a wire.
00:04:48So it is assumed that you have a very long wire. For all practical purposes.
00:04:52You can think of this as an infinite wire and then
00:04:58you can try to ask about them the magnetic field lines.
00:05:02It turns out that the magnetic field lines are concentric circles like that.
00:05:07Here, I'm assuming that the current
00:05:18goes from goes from down to up and in this case, the magnetic field lines,
00:05:22our counter clockwise.
00:05:30So the magnetic field, like the electric field, is a vector quantity,
00:05:34so you need both a magnitude and the
00:05:40direction in order to designate the magnetic field.
00:05:42So for the infinite wire,
00:05:46if there is some current I that passes through the wire,
00:05:49then it turns out that the magnetic field is given by the following expectation.
00:05:53It is new, not which is the constant.
00:05:59I'm going to tell you about this constant in a minute
00:06:01times the current I divided by two pi divided by our
00:06:03what is our our in the distance between the wire and
00:06:10the position you are interested in finding the magnetic field at,
00:06:16but there remains to specify in the direction.
00:06:22So this is the magnitude of the magnetic field. What is the direction?
00:06:25I will take the direction
00:06:31to be the counter clockwise direction and I will call it the theatre.
00:06:34So this is my direction.
00:06:39If it's a hat, it's a hat is called a unit vector in this counterclockwise direction.
00:06:46So if it's a hat,
00:06:53man in the magnitude of
00:06:56the heart is equal to one.
00:06:57So now we specified the magnetic field as the magnitude and the direction.
00:07:02Of course, we are using the S i units.
00:07:08So in S I units, the magnetic field will be measured in Tesla.
00:07:11And of course, the current is measured in amber
00:07:17and are,
00:07:25which is the distance between the wire and the position we are
00:07:27interested in finding the magnetic field at is measured in metres.
00:07:32Mu not is a constant of nature called the affirmative itty of the vacuum.
00:07:37And this is given by the following Gap number It is four pi times 10 to the minus seven
00:07:45Newton. There compare square.
00:07:55Alright, so let us also do one more example Instead of having an infinite wire,
00:08:02there is a wire that is paint in the shape of a
00:08:08circle and there is some current I that flows through the wire.
00:08:11Now the expression of the magnetic field is complicated,
00:08:16so I am not going to write a mathematical expression.
00:08:19Instead, I am going just to draw the field lions.
00:08:22You might ask how we can find them this magnetic field lines.
00:08:28If you want to do that, you actually need to apply something called
00:08:33Joseph our law. It is beyond the scope of this very quick crash course.
00:08:37However,
00:08:42I'm just telling you that in principle you can use Pedrosa for law
00:08:43in order to compute the magnetic field at any point in the space.
00:08:48And from there you can draw the magnetic field lines.
00:08:52So, uh, we discussed the concept of the magnetic field.
00:08:59We I showed you, uh, how you can draw the magnetic field.
00:09:04Lyons, uh, from a piece of a natural magnet.
00:09:10Then from a wire that is an infinite wire,
00:09:14and then the magnetic field lines of a circular wire.
00:09:18Uh, in the next section,
00:09:23we are going to use the concept of the
00:09:25magnetic field in order to compute the magnetic force.
00:09:28
Cite this Lecture
APA style
Anber, M. (2022, January 12). 4. Electricity and Magnetism - Magnetic Fields [Video]. MASSOLIT. https://massolit.io/options/4-electricity-and-magnetism?auth=0&lesson=4438&option=14480&type=lesson
MLA style
Anber, M. "4. Electricity and Magnetism – Magnetic Fields." MASSOLIT, uploaded by MASSOLIT, 12 Jan 2022, https://massolit.io/options/4-electricity-and-magnetism?auth=0&lesson=4438&option=14480&type=lesson