MAGNETISM

MAGNETISM

 CONCEPT

It is part of physics that studies the properties of magnets. These properties are manifested by some minerals such as iron, cobalt, nickel, steel, etc. Best known for their magnetic properties is the mineral magnetite (Fe₃O₄).

Magnets are objects that enjoy two important properties:

1. Attract iron. In this sense, some substances such as steel or metal alloys in weak become permanent magnets when placed near a natural magnet for a certain time. Then they say the substances are magnetized.

2.- Oriented in a particular direction in space. For example when iron filings are sprinkled near a bar-shaped magnet, these iron filings group forming specific lines.

                                      

3. The ends of the magnet are called magnetic poles or poles of the magnet, which is where external magnetic effects of the magnet are concentrated, there greater accumulation of iron filings appear.

The concentration of these poles in the magnet are at a distance from the ends of the magnet equivalent to 1/12 of the length of the magnet.

                                                                              

The pole that is oriented to the geographic north is called north magnetic pole (N), the other is called south magnetic pole (S), and the intermediate part is called neutral zone.

If you have a magnetized iron rod and it is suspended by a thread in its central part, it tends to align with the north-south direction; from this we can also understand the ordinary compass whose needle is just a piece of magnetized iron.

4. The same poles repel each other and opposite poles attract each other.

5. An electric current creates a magnetic field in the surrounding space, and this action affects near objects without touching them.

 The following graph shows a case where a electric current flows through a conductor wire, which perpendicularly intersects a plane, in this case a paper, which has been sprinkled with iron filings that are oriented along concentric circular paths . These geometric paths are called "lines of magnetic induction," which graphically represent the magnetic field that surrounds the conductor wire.

Loss of magnetic properties

A magnet can lose their magnetic properties due to two reasons:

1. When it is heated up to a certain temperature, which is known with the name Curie temperature.

Iron.......750^oC
Ferrite...218^oC
Nickel...350^oC

2. When it's hit, since it can produce a molecular disorder.

Inseparability of the poles

If a magnet is cut into two parts, each of the portions obtained constitute a new magnet, and that means with its own north pole and south pole. And this incident may continue until the molecular level, so that a molecule with magnetic polarity comes to be called molecular magnet.

In the atomic theories of matter and quantum mechanics, it's said that microscopic currents exist and are associated with the movement of electrons around the nucleus of the atom and the electron spin, which means a type of rotation of the electron on its own axis.

LAWS OF MAGNETISM

Qualitative law

External magnetic poles of the same name repel and the ones of different name attract each other.

Quantitative law

The law states that the force of attraction or repulsion between two magnetic poles is directly proportional to the product of the intensities of the magnetic poles and inversely proportional to the square of the distance between them.

 Where

F: Force of magnetic attraction or repulsion.

K: Constant, whose value depends on the system of units.

u: magnetic permeability. It has no units and its value depends on the medium in which the magnetic poles are located.

m: Intensity of the magnetic poles or magnetic mass.

d: distance between external magnetic poles.

Units:

 

Magnetic constant ( μ_o )

The coefficient "K" in the international system can be written as:

The magnitude μ_o is called the magnetic constant and its value is:

Unit of Magnetic Pole Strenght

Amper x meter (A.m):

In the International System it is defined as the magnetic mass that acting upon another like it in the vacuum and with one meter of distance, they repel each other with a force of 10^-7N.

[Magnetic mass] = [A.m]

The magnetic permeability in the vacuum is equal to unity (μ=1) and in the air has approximately the same value.

   

MAGNETIC FIELD

CONCEPT

 

It is a property of matter as a result of moving electric charges (electric current). The magnetic field is the geometric place where the magnet affects with their magnetic effects on another object with magnetic mass or on moving electric charges. In that sense the magnetic field exerts its force (F).

Notably, the magnetic field is a vector field thus a vector quantity associated with each point in space. To represent the magnetic field the symbol B is used.

LINES OF FORCE
 

They are such geometric lines that serve to represent graphically the magnetic field. In a magnet the lines of force emerge from the north pole (N) and enter the south pole (S); the latter is done by convention.

 

 

The magnetic force F that acts over a positive charge, moves with velocity v and  is perpendicular to the magnetic field B and v. The force is greater when v and B are perpendicular.

a) Given a charge moving parallel to the magnetic field experiences a zero magnetic force.

b) If a charge moves at an angle θ with respect to a magnetic field, it will experience a magnetic force of magnitude:

Note that F is perpendicular to the plane containing 

 

c) If a charge moves perpendicular to a magnetic field, it will experience a high magnetic force with magnitude

 

Calculating the direction of the magnetic force on a moving charged particle.

a) The right hand rule for the direction of the magnetic force on a positive charge moving in a magnetic field:

- Place v and B in such a way that they were attached to their origins.

- Imagine that v is turned to B in the v-B plane.

- The force acts along a line that is perpendicular to the plane v-B. 

Gyrate the fingers of the right hand around the line. In that sense, the thumb points in the same way as the acting force.

b) If the charge is negative, then the direction of the force is opposite to the one made with the right hand rule.

The unit of the International System for B is equal to 1 ns / cm, due to the fact that one ampere is a Coulomb per second (1 A = 1C / s), 1N / Am. This unit is called tesla (T):

1 Tesla = 1 T = 1 N / a.m

* The instruments used to measure magnetic fields sometimes are called Gaussmeters. A gauss (1G = 10^-4 T) is another unit B that is also commonly used.

* The magnetic field of the earth is approximately 10^-4T, ie, 1G.

* Inside the atoms are magnetic fields of the order of 10T, which are of great importance in the analysis of atomic spectra.

* It is likely that the magnetic field on the surface of a neutron star is about 10⁸ T.

MAGNETIC FIELD STRENGTH (H)

It is a vector physical quantity used to describe the magnetic field. Its value is defined as the resultant magnetic force acting per each unit mass at a point in a magnetic field.

The vector intensity of the magnetic field has the same direction of the resultant magnetic force.

Where:

M: Magnetic mass north or south, creator of the magnetic field.

m: Magnetic mass north, the magnetic field detector.

From the quantitative law, the value of the force is replaced and we obtain.

Representation of the magnetic field strength

The tangent to the line of magnetic force has the same direction of the vector magnetic field strength at that point and is unique, therefore, the lines of forces are not cut.

H1: Due to North Pole

H2: Due to South Pole

mo: North test. Magnetic mass.

H = H1 + H2

In the case of a magnet, their north and south magnetic masses are equal.

Mnorth= Msouth = M

Pair of forces on a bar magnet in an external magnetic field where a force on the north pole and the other on the south pole origins, equal in magnitude and opposite in direction, that tend to align with the external uniform magnetic field, forming a couple of forces whose value is equal to the product of one of the forces multiplied by the perpendicular distance between the forces.

* Cupla: couple of forces

Cupla = C = F. D Seno

MAGNETIC FLUX (ϕ)

It is defined as the product of magnetic field strength H and the surface A perpendicular to the lines of force of the field.

  ϕ=H.A

Where ϕ is the number of lines of force.

If the surface was inclined to the lines of force, then according to the graph:

ϕ =H.A.Cosθ 

Units

The magnetic flux in the International System (SI) is measured in "weber". The unit of the SI for the magnetic flux is equal to the unit of magnetic field (1T) multiplied by the unit area (1m²).

Observation:

* It should be noted that the magnetic field lines never have endpoints, unlike the electric field lines that begin and end in electrical charges. Although it appears that the magnetic field lines start at the north pole and terminate at the south pole, actually the field lines of a magnet pass through its interior.

Magnetic induction (B)

Also called magnetic flux density. It is that vector that is used to write the magnetic field. Its value is defined as the number of lines of force that perpendicularly cross through the unit area of a surface located in the magnetic field.

If θ = 0^⁰ then the lines of force are perpendicular to the surface.

Magnetic Permeability (μ)

It is a dimensionless magnitude and its value indicates the behavior that experiences a substance when it is located within an external magnetic field. In that sense, the magnetic permeability indicates if the dispersed substance concentrates or not alter the magnetic field or the lines of force.

It is defined as the quotient of the magnetic induction (B) and the magnetic field intensity in the vacuum.

Units:

1. Paramagnetic Substance (μ _≥1):

They are those substances that when being inside a magnetic field weakly concentrate the lines of force or they just don't alter them. This type of substance has constant magnetic permeability slightly greater or equal to unity. Examples are aluminum, platinum, air, vacuum, etc.

2. Diamagnetic Substances (μ <1):

They are those substances that disperse the lines of force in an external magnetic field, so that they magnetize in an opposite sense to the inductor magnetic field. Such a substance has constant magnetic permeability and its value is less than one. Examples of them are antimony, bismuth, water, etc.

3. Ferromagnetic Substance (μ >1):

They are such substances that in an external magnetic field concentrate the lines of force, so that they magnetize for the inductor magnetic field.

These substances have varying magnetic permeability much greater than the value of one. Examples are iron, nickel, cobalt, etc.

Illustrative examples

1. A particle of mass m and charge q enters a square region  where there is a magnetic field perpendicular to the region, with a velocity 18x10⁴m/s. If q/m = 0,18x 10¹²

C / kg. For which side of the region the particle scapes?

 

 

If

B=1G=10^-4 T

Then:

 

By plotting the path of the particle is obtained:

 

In that sense, the particle scapes by the side GF

2. An electron inside a particle accelerator obtains a kinetic energy of 239.1 keV. It enters perpendicularly to an uniform magnetic field with 0,4T. What is the radius (in mm) of the resulting circular path? 

me= 9,1 x 10^-31kg

We know that:

Then:

1ev= 1,16 x 10^-19 J

B = 0,4 T

E_c = 239,1 Kev

We also have that:

 

In that sense, the radius of the resulting circular path is 4,1 mm

3. The magnet is attached by a rope ab from one of the magnetic poles. The intensity of each pole of the magnet is equal to 3A.m and its weight is W = 24N. If the system is within an external magnetic field, uniform and horizontal with Intensity M = 4 (A / m) and the figure shows a magnet bar in equilibrium. Find the angle theta which define the equilibrium position.

 

When applying the second condition of equilibrium with respect to point A.

 

 

4. Determine the intensity of the magnetic field generated by a bar magnet in the points of the circumference shown. The separation distance between the magnetic poles is "2a", and the magnetic masses of the north and south poles are equals to "m". The value of magnetic intensity should be expressed in terms of angle θ.

 

From the graph:

 

 

Then:

 

INTERESTING NEWS ABOUT MAGNETISM

JAPAN’S MAGLEV TRAIN HAS BROKEN WORLD SPEED RECORDS BY HITTING 603 KM/H

The experimental train called Maglev broke records by hitting 603 km/h (374 mph). This train runs on magnets rather than wheels. It works with the principle that when magnets are pushed together (north/north) or (south/south), they repel each other.

The Maglevs (Magnetic Levitation trains) have magnets in the bottom and they are repelled from the track below that is also magnetic, then the train floats 10 cm above the ground so that there is much less friction, hence it can reach such great speeds.

 BBC (2015, April 21). newsbeat. Japan's Maglev: Slower than a bullet, faster than wind. Retrieved from http://www.bbc.co.uk/newsbeat/article/32393166/japans-maglev-slower-than-a-bullet-faster-than-wind