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- What's up? Electronics here, and you are here to learn all about magnetic fields, so let's go. Okay, how can we
- visualize this whole thing? Well, let's imagine a conductor with a current flowing through it. If I bring magnetic
- needles near this conductor, they will align themselves in a specific direction. And if I plot the direction
- for many of these needles, they follow a clear path, namely around the conductor. It has been established that
- field lines outside a magnet always point from the north to the south pole. However, to determine the direction of
- this magnetic field, we use the right-hand grip rule. In doing so, our thumb points in the direction of the
- current, and the curve of our fingers indicates the direction the magnetic field curls around the conductor. If I
- look at coils, I can imagine that a much stronger magnetic field is generated, because I have, in quotes,
- many more conductors creating a field, even though it's practically just one single wound wire. The field strength
- was determined by placing twisted magnetic needles into the field and seeing how much torque was needed to
- align them with the field. When this was done in a toroidal coil, it was found that the entire torque was
- proportional to the current and number of turns, and inversely proportional to the mean length of the coil L. Thus,
- the following material-independent expression for field strength was obtained. H = I times n divided by L,
- though the term field strength can be confusing here, as H does not directly indicate the strength of the field,
- since H is material-independent and different materials result in a stronger or weaker field. Rather, H
- simply indicates that a field is being generated by the current at all. How strong it is depends on the material
- used inside the coil, and we'll learn about that shortly. What we can also note is that the numerator of H
- corresponds to our magnetomotive force Theta, which is I times n. Yes, and as I already said, our field strength H
- does not provide information about how strong the magnetic field is at a specific point. Therefore, the quantity
- B, magnetic flux density, was introduced. And how to determine it was shown by the following experiment,
- where a current-carrying conductor of length L was placed into this B-field, and it was discovered that a force acts
- upon this conductor. My force was the product of flux density, current, and the length of the conductor, and the
- directions were derived from the right-hand rule, also known as the CMI rule; where CMI stands for Cause,
- Mediation, and Impact, with the cause being the current, the mediation our B-field, and our middle finger then
- pointing in the direction of the impact force F. This is how we incorporated B into an equation that simultaneously
- represents the field strength, because the higher my flux density, the greater my force. So, we now know how the force
- depends on the B-field, and our B-field depends on the magnetic field, i.e., our field strength, as follows: B = µ*
- H. And this mu is composed of µ0 times µr, where µr depends on the material and µ0 represents the permeability of
- free space. It is also important to reiterate that all these quantities— the B-field and the H-field—are
- directional, meaning they are vector quantities that possess not only a magnitude but also a direction. If flux
- density indicates how much flux flows per area, then my magnetic flux is logically flux density times area. The
- unit is the Weber. For magnetic tension , at least in a homogeneous field like this one, it can be stated that the
- magnetic tension is our field strength times the distance between these two surfaces. So, H times s. Let’s take a
- closer look at Ampere's circuital law and recall that the field strength equals NI/L, where our number of turns
- is 1 here, since we are only considering one conductor, and our length L is naturally 2πr. If I want
- to calculate my magnetic tension along an arbitrary integration path, I have to take the line integral of the
- different field strengths all the way around this entire integration path. That is obviously super messy and ultra
- complicated, so nobody actually does that. We make life easier for ourselves , of course. Someone discovered that
- the integration path actually doesn't matter. We can therefore simply take a normal circle around our conductor. And
- if I move along a circle, as you can see at the top left, then at every point on this circle our field strength
- is constant, because logically our field is a circle, and our complicated line integral simply becomes the
- product of the field strength and the path 2πr. And using the equation on the left, we can show that this is also
- equal to I. This means nothing more than that the line integral of the magnetic field strength is equal to our
- electrical current linkage, Theta. So, if I have a surface with perimeter L, my Theta simply tells me the sum of all
- currents entering and exiting through this surface. Right, and now let’s quickly wrap up magnetic circuits with
- what we’ve just learned. If we now look at our area bounded by L1, our Ampere's Law tells us that our
- magnetomotive force here is simply the number of turns times the current, because our area is penetrated by this
- current. The formula for magnetic reluctance is L over mu A, where L is naturally the mean length of the
- material through which the magnetic field passes. A is the cross-sectional area and mu is the material-dependent
- constant we already discussed. This leads us to our Ohm's Law for the magnetic circuit. Ohm's Law is U equals
- R times I, and here it is translated into theta equals R sub m times phi. This means our theta is equal to the
- magnetic voltage. We already learned that in Ampere's Law just now. Our R sub m is simply our magnetic reluctance
- and our phi is analogous to the electric current. That means, just like in DC circuits, we can set up and
- calculate circuit diagrams with this knowledge using the very simple rules we already know. And I hope that I have
- been able to convey some basics about the magnetic field to you, with which you can now tackle my practice problems
- . Have fun with them. Your Elektronic. Yes.