Theory of Magnetism, Electromagnetism and Magnetic Flux

Magnetism:

A small number of materials in nature show the property termed as magnetism. The consequence of magnetism first being introduced is usually attributed to the Chinese in the 3rd century BC. A naturally occurring magnetic material termed as Lodestone, a specific crystallised form of the mineral Magnetite as shown in figure below, was later discovered by the ancient Greeks. The other naturally occurring magnetic material is Pyrrhotite that is an Iron Sulphide mineral. However, the Earth itself as well possesses a magnetic field and magnetised materials eagerly interact with this, as for illustration the needle of a compass.

This is generally as well known that other materials are simply magnetised whenever subjected to the influence of a strong magnetic field and that whenever the field is eliminated they retain a large degree of magnetism on long-term. These materials are elements such as Iron, Nickel and Cobalt, and man-made materials like Ferrite that is an Iron-Ceramic compound. Man-made permanent magnets are generally made up from Iron or Steel. In Electronic Engineering, Ferrite is generally employed as a core for inductors and transformers.

In the structure of an atom, the numbers of electrons and protons are same and therefore the associated charges cancel and hence elements are electrically neutral. The Electrons rotate in orbits at specific energy levels around the nucleus and at similar time spin on their own axes, instead similar to the Earth’s orbiting around the sun and yet spinning itself. The charged particle in motion, like an orbiting electron, consists of a miniscule magnetic moment related with it. Each and every energy level can contain two electrons and whenever they take place in pairs they orbit and spin in opposite directions and therefore the magnetic moments cancel out.

Materials that become easily magnetised have an odd number of electrons. This signifies that there is one electron, in the outermost orbit of the atom, with a direction of orbit and spin that is not counterbalanced by the second electron. This gives mount to a net magnetic moment. In magnetic materials some thousands of molecules of the material join into a domain where the miniscule magnetic fields of individual molecules align to provide a stronger field. Beneath the right conditions the domains then align in the material and hence the magnetic fields add cumulatively to provide an overall magnetic field related with the piece of material. When a piece of magnetised material is suspended in free space it will align with Earth’s magnetic field. The North-seeking end of the material is termed as the North Pole (N) of the magnet whereas the South-seeking end is termed as the South Pole (S).

Magnetic Flux:

Let consider a permanent bar magnet with North and South poles aligned as shown in figure below. Magnetisation of the material generates an Energy or Force Field in the vicinity of magnet. That is, any material subject to magnetism is placed in this field will experience a force. The field can be symbolized by lines of flux that show the intensity and direction of the force as indicated in figure below. This is important to note that such lines are imaginary or illustrative however nevertheless do symbolize a definite experienced effect. The lines are termed to as lines of Magnetic Flux. The intensity of the field is generally represented by the density of lines and arrows which are employed to show the direction. This is admirably stated by the classic Iron Filings Experiment, where iron filings are sprinkled on to a page positioned over a bar magnet as shown in figure below. The stronger the magnet is, the greater the intensity of field and the greater the density of the lines of flux in a given space.

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Figure: Lines of Magnetic Flux   

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 Figure: Iron Filings Experiment

There are number of basic axioms or rules related with the lines of magnetic flux as:

A) Lines of magnetic flux form the closed loops.

B) The lines of flux never intersect.

C) The lines of magnetic flux flow from south to north in the magnetic material and from north to south exterior of it.

D) They usually flow in straight lines in the homogeneous material and in curved ellipsoids exterior of it.

E) The parallel lines of flux running in similar direction repel each other whereas those running in the opposite directions attract each other.

The nature of magnetic field related with a magnetised source can as well be altered by adding one or more additional sources. The fields of all sources interact to make a modified resultant field that depends on the directions and strengths of individual fields. Rule between magnetic sources is that:

“Like poles repel each other while unlike poles attract”.

Definitions:

The Magnetic Flux is defined as the lines of force illustrating intensity and direction of a magnetic field.

Magnetic Flux is represented by the symbol ? and has units of Webers (Wb). This unit is termed after a German physicist Wilhelm Eduard Weber (1804 – 1891).

Magnetic Flux Density is a measure of intensity of a magnetic field. This is defined as the quantity of magnetic flux passing via a unit area perpendicular to the direction of field.

Magnetic Flux Density is represented by the symbol B and has units of Webers per square metre (Wb/m2) or more accurately Teslas (T) named after a Serbian-American inventor and electrical/mechanical engineer Nicola Tesla (1856 -1943).

Magnetic Flux Density = Magnetic Flux/Area, B = Φ/A Wbm2 (T)

Magnetic Flux = Magnetic Flux density x area, Φ = BA Wb
   
Examples:

Example: A bar magnet has dimensions of 8cm x 2cm x 1cm and possesses a net magnetic flux of 25Wb. Find out the density of magnetic field experienced near to a pole face of the magnet.

Solution:

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Area of pole face, A = 2cm x 1 cm = 2 x 10-2 x 1 x 10-2 = 2 x 10-4 m2

Density of magnetic field is the Magnetic Flux Density B,

B = Φ/A = 25/(2 x 10-4) = 12.5 x 104 Wb/m2 (T)

Example: The magnetic rod employed in the aerial of an AM radio is made up of magnetised ferrite material containing a total volume of 10cc. The ferrite is uniformly magnetised to contain a flux of 1.25 mWb/cc of material. The aerial should possess an internal magnetic field intensity of 120T in total. Find out the dimensions of the rod needed. 

Solution:

The net flux possessed by the ferrite aerial is the flux per unit volume of material times the total volume of ferrite employed and hence:

Φ = 1.25 x 10-3 x10 = 1.25 x 10-2 Wb

The overall intensity of the magnetic field produced in the aerial is the magnetic field intensity B and hence:

B = Φ/A

A = Φ/B = (1.25 x 10-2)/120 = 1.04 x 10-4 m2

The area of rod is given as πr2 where r is the radius of the rod.

Πr2 = A

r2 = A/Π = (1.04 x 10-4)/3.14 = 3.31 x 10-5 m2

And hence,

r = √3.31 x 10-5 = 5.76 x 10-3 m = 5.76mm

The length of aerial required l, can be found from the radius and volume:

V = Π r2 l

l = V/ Π r2 = (10 x 10-6)/(1.04 x 10-4) = 0.096 m = 9.6 cm

The dimensions of the requisite ferrite rod are thus:

Diameter d = 2r = 1.15 cm
Length l = 9.6 cm

Electromagnetism:

Whenever electric current flows in a conductor (that is, metal), free charge carrying electrons are in motion. This outcomes in a magnetic field being produced around the conductor as was discovered by a Danish physicist and chemist Hans Christian Oersted (1777 – 1851), in the 19th century.

There is a convention for exhibiting the direction of current in the conductor whenever viewed end-on as illustrated in figure shown below. A dot is employed, corresponding to the tip of an arrow, to point out the current flowing towards the observer, while a cross is employed, corresponding to the end feathers at the back of an arrow, to point out the current flowing away from the observer. This can be observe that the direction of magnetic field around the conductor is clockwise if viewed with the current flowing away from the observer and anti-clockwise if viewed with the current flowing in the direction of observer.

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      Figure: Current Flow conventions and related Magnetic Fields

Right Hand Screw Rule is a means of finding out the direction of magnetic field surrounding a current carrying conductor as shown in figure below. It is stated as follows: When the conductor is grasped in the right hand with the thumb facing in the direction of current flow then the fingers point out the direction of the surrounding magnetic field.

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Figure: The Right Hand Screw Rule

If the current carrying conductor is made into a loop then the magnetic field around the conductor can be seen to orientate therefore as to pass via the loop as shown in figure below. As can be predicted, intensity of the field will depend on the area of loop and magnitude of the current flowing in the conductor. This will be directly proportional to the current and inversely proportional to the area of loop.

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Figure: The Magnetic Field prepared through a Current Carrying Loop

This principle can be extended by winding a conductor, frequently on an insulated former, and hence several conducting loops are made side-by-side to build a coil.

In this case the magnetic fields related with the individual loops combine and hence a strong longitudinal magnetic field can be produced acting via the coil as shown in figure below. This is basically the principle of an electromagnet where an electrical source is employed to give current via the coil and this current then forms a magnetic field. Whenever the current ceases to flow, the magnetic field disappears. This principle can be exploited in a broad range of electromagnetic devices and applications.

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Figure: A Wound Coil producing an Internal Magnetic Field

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