Electromagnetism

bee-Mayan

The magnetism was shortage in old Greece in the Magnesia locality of Thessaly around year 800 aC when they found that a mineral (the magnetite) presented an attraction action on metals that iron had.  This mineral has a very high percentage of iron (on 72%)

Nowadays, the magnets widely are used in electronics (loudspeakers, alarm systems, detectors, etc). Before we already used it the animal, between which are molluscs and bees, in order to orient ourselves in the space. A bee can cross great distances, return to the panel and indicate to the rest with a ritual of movements, where it is the pollen center. Others as the doves, have small magnetite pieces located in the tip, that serves to him as compass to orient itself.

neodymium

Neodymium. There are permanent magnets developed by the man (General General Motors, 1982), whose power to attract ferric elements is much more powerful and have replaced to traditional magnets. Now very they are used in hard disks, motor electrical, tools without cables, etc.

In the text book we have some basic definitions that are:

  1.  The Magnetism is the property that has certain materials (magnets) to attract ferromagnetic compounds (that have iron)
  2. The line of force is the representation that we make to indicate that magnetism exists and are closed, with exit in the North Pole and entered by the south of the magnet
  3. Magnetic flux (Φ) is the line number of force that we have in the magnetic field and it is moderate in Weber
  4. The magnetic induction (b) is the amount of lines of force that happen through unit of perpendicular surface to the direction of the lines of force and it is moderate in Tesla.
  5. In the image of the left, we have placed a surface with an inclination with respect to the lines of force (angle represented by θ). Within the zone of surface in green, they are going to leapfrog a series of force, that will be greater to smaller value of the angle. The relation between the value of B magnetic flux comes given by
  6. , that in the vectorial form, is of the form vectorial flow
  7. For a determined field, B always is the same and it does not vary. Another thing is that we have a turn within the field that as a result of a turn, the surface is picking up line of field€ and the flow is changing throughout the turn. R

We have represented the lines of force in blue that cross a surface in green. That surface has a vector S that indicates the inclined thing that it is with respect to the lines of force. It is as the mast of the surface. If he is parallel with the lines of force, they enter but line in the green surface and therefore the gathered flow is greater. If he is perpendicular to the lines of field, the lines that enter the surface are zero. In order to consider this circumstance within the formula, we must say that:

sine-and-cosine

There are two important mathematical functions of trigonometry that we must know. One of them is the function sine and the other the function cosine. If we represented in a coordinate axis a vector of radio 1, (r = 1), the projection that has that vector with the axis and, depends on the angle Î±. The value of the shade€ on the axis and is obtained calculating the sine Î±. In the same way, the shade€ on x-axis has when calculating the cos Î±.

Permeability and Intensity of field

As it happens with the electricity, (when we have several ways possible for electrons, these take the way from smaller resistance) the line of field, before several ways, take the way around which they circulate with greater facility .

Each material behaves of different way. For example the air behaves worse than the iron for the lines of field. That characteristic is called permeability, imagines by the letter µ and on the basis of its value, we have:

  • Ferromagnetic
  • Paramagnetic. The paramagnetic materials have magnetic permeability similar to the one of the emptiness.
  • Diamagnetics. It is a property of the materials that consists of repelling the magnetic fields. He is the opposed thing to the paramagnetic materials.

If for the emptiness, the permeability has a value of 4 * Π * 10†‘ -7 H/m, for the iron is 5000 times greater.

This gives rise to another denominated variable Intensity of field, that imagines by the letter H and that is very used in electrical engineering (motor, transforming, etc)

intensity-of-field

We see the utility. If we have a two transformer that uses boninas and a ferromagnetic material (in this case, a toroid), that has a coil of N turns around which a current circulates and the toroid has an average length of l, the Induction that we have in the toroid will be greater if we have a material of good permeability. The calculation of B in this case is:

Electromagnetism

This word, electromagnetism, come thus formed by the physical phenomena that take part, that is electricity and magnetism, since both are related, as it verified the Danish physicist Oersterd at the home of century 19.oersted-experiment

This scientist made pass a current through a cable and verified that a magnetic needle was placed perpendicular to the direction of the current.
The current creates some lines of field that are circular with the sense of the law of the corkscrew€.

The law of the corkscrew is applied of the following way. The corkscrew in the cable and tour is put so that the advance of the corkscrew with the sense of the current agrees. The lines of field that are generated have the turn of the handle of the corkscrew.

campo_corriente_brujula

In this image we have a perpendicular cable to the plane whose current leaves the plane (marked by a point). Applying the law of the corkscrew, the lines of field turn race against the clock.

It is possible to be visualized the lines of magnetic field if we put small compasses, that are oriented so that the lines of field enter by the South Pole and leave by the north.

 

Law of Faraday

experience-of-Faraday

Like a current can produce a magnetic field, a magnetic field by which an electrical cable moves produces an electrical current.

One is fulfilled that when through a returned turn of N it passes a variable field B, takes place a difference of potential in the tips of the turn and, therefore, a circulation of electrical charges. It formulates it comes given by:

This formulates says us that the tension that appears in the ends of the coil is equal to the returns of the coil multiplied by the variation of the flow with respect to the time. In case the magnet is quiet, the magnetic flux exists but it does not vary with respect to the time because we have the immovable magnet and, therefore, I complete term is worth zero, reason why the tension is zero.

In order to know but. For most peculiar, this interesting video of electromagnetism.

coilCoils.

Once we understand the basic concepts of the electromagnetic field, we will see a passive component very used in electronics that is the coil, composed of a series of turns that surround to a nucleus (it can be air or some ferromagnetic material). In the case of the figure, the nucleus is air.

The behavior of the coils is similar to the one of the condensers, but in this case, instead of being against to that change abruptly the tension, is going away to oppose to abrupt changes of the current. The reason is due to the coefficient of autoinduci³n of the coil, that is defined as the variation of the flow with respect to the time.

It formulates it previous indicates an important value to us in all coil that is the coefficient of self-induction (l) and it is moderate in Herios. The previous expression says us that f.e.m of the coil depends on the variation of the flow with respect to the time and also is equal to L by the variation of the current with respect to the time. We will see an example.

Example 1. To calculate f.e.m of self-induction that appears in the tips of a coil of 100 miliherios if by the same a current grows gradually from or to 20 Amperes in 10 milliseconds

Solution: 

law Faraday

Exercise 1. To calculate the value of tesi³n induced in a coil of 200 returns, if taeda 200 mS in happening between the poles of the magnet of the image, from the outer zone, with smaller magnetic flux (5 * 10 -3 Wb) to internal other but with major Φ, of value 8 * 10 -3. Weber

To calculate the intenshelpad measured by the ammeter To, if the resistance is 10 Ω. Solution at the end of the page.

2 Calcula fem and the induced current intensity in a rectangular turn of 5cm Faraday-coil

of side, whose resistance is of 15 ohms, when a magnetic field uniform of 0,4 T crosses it perpendicularly and the turn turns a quarter of return around its diameter in a time of 0,1 s

3  terrestrial field

A squared coil of 30 cm of side has 10 returns. The value of B comes dice by 0,2 Wb/m2.  We rotate the turn vertically, so that primcipio lines of field do not enter, and to the 90 degrees of its turn, perpendicular to the lines of field appears (maximum flow). All this in a time of 0,150 s. To calculate
  1. What is fem induced
  2. Induced current if the resistance of the coil is of 2 Ω
  3. To draw how it would be the tension generated in tips of the coil when a complete turn of the turn has taken place. For it, in the axis of abcisa to represent the turn in degrees and ordinates (axis Y) the created tension.

It is possible to be demonstrated that the association of the coils for circuits series and parallels comes given by the formulas:

(For the connected coils in series)

 If they are connected in parallel

SOLUTIONS

Apliacando the induction formula, we have

fem = N * (dΦ/dt)

We replace values, whereas clause that dΦ is the variation of the flow in the coil in the 200 milliseconds, therefore

jerci1

 

 

Applying the law of Ohm, we have current it is V/R, or 3/10 = 0,3 A

Data:

  • B=0,4T
  • l=5cm=0,05m.
  • R=15 Ω
  • t=0,1s

We apply formulates it where the variations of the magnetic flux based on the passed time are considered. In the end, the flow is zero, and therefore Φ=0.

At the home, the flow calculates by the formula Φ = B * S

First it is to calculate the area of the turn. As it is squared, it is side by side, that is 5*5 = 25 cm2 or what is the same, 0.0025 ms2

We arrive at that we have a flow of 0,4 T * 0.0025 0.001 ms2 = W

We apply to the formula fem = N * (dΦ/dt) and have the following result:

Faraday ejercicio2

When dividing that tension, by the resistance, we have the intensity:

10 Is = mV/15 Ω = 0.666mA

3Las solutions are:

  1. Tension 1.2 volts
  2. Intensity = 0.6 A
  3. Sine signal with values of tip calculated o'clock 1