Production And Application Of Magnetic Fields By Electric Current Flow

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Discovery of Magnetic Field around Conductors by Hans Oersted

Hans Oersted a physic professor discovered that all the conductors that do carry currents has a magnetic field around it in the year 1820, this discovery has shade more light on the on the origination of magnetic field  from a flow of charges.

Hans Oersted through his experiment detected that if he allowed electric current to pass through a conductor near a spontaneously compass needle that is suspended, then the compass will be observe to deflect, in the same point if the current is allowed through a conductor that can easily be moved and placed close to the bar magnet, then the conductor will experience a force that is at a right angle to the conductor.

If we take the magnetic field direction to be the direction of the force on the north pole of a compass needle, Oersted observed that the magnetic field is in the form of concentric circles that surrounds the current.

The exploration of magnetic effect on an electric current has led to more discoveries of numerous electronic devices that are used in daily day to day operation by mankind.

This paper will address on the production of magnetic fields by the flow of electric current and its application.

It is always noted that when two magnets are taken close to each other they will either attract each other or repel each other as per the respective orientation, similarly if you place a bar magnet on a piece of paper, the iron filling get attracted and scatter around the magnet in structure line magnetic field that is surrounding an electric dipole.

Is the region or space where magnetic influence is felt around a magnet (Roger, 196, 7-8).

The first definition of the electromagnetic field in the presence of non-trival Higgs background was given by t’Hooft where he introduced magnetic monopoles in a SO(3) Georgi-Glashow model.

The definition was presented as

From the above presentation G ^a_µ  W ^a_µ - W ^a, where
(^a are the Pauli matrices) represents  a unit isovector that defines the "direction" of the Higgs field in the SO(3) isospace (this coincides with SU(2)) and (D_µ)^a = _µ^a + g ^abc W_µ^bc.

Where W_µ^b are the gauge fields components in the adjoint representation. In other models, like the one being considered by t'Hooft, a topological obstruction will prevent this kind of operation to be possible everywhere. In this case singular points (monopoles) or lines (strings) where  ^a = 0 appear, which become the source of magnetic fields. t'Hooft result provides an existence proof of magnetic fields produced by non-trivial vacuum configurations.

Concentric Circles Surrounding Electric Current Result in Magnetic Field

A general definition for the Weinberg-Salam model was given by Vachaspati which states

D_µ = _µ - i[(g) / 2] ^a W_µ^a -i[(g') / 2] Y_µ.

From this expression Vachaspati to argued that magnetic fields will be produced during the EWPT.

The contribution to the electromagnetic field produced by gradients of ^a can be readily determined by writing the Maxwell equations in the presence of an inhomogeneous Higgs background

On dimensional grounds, D  ~ v /  where v is the Higgs field vacuum expectation value, Vachaspati concluded that magnetic fields should have been produced at the EWPT with strength

The case of a EWPT

For the SU(2) gauge fields we have

Where the isovector ^a this equation reads

In general, the unit isovector ^a can be decomposed into

where ^T₀  - (0, 0, 1). It is straightforward to verify that in the unitary gauge,  reduces to ₀. The relevant point in the equation is that the versor [^(n)], about which it is performed the SU(2) gauge rotation, does not depend on the space coordinates, this equation of motion becomes

As expected, we see that only the gauge field component along the direction , namely A_µ = n^a W^a_µ, that has some initial dynamics which is created by a nonvanishing gradient of the phase between the two domains.

In principle, in order to determine the magnetic field produced during the process, we will require a gauge-invariant definition of the electromagnetic field strength in the presence of the non-trivial Higgs background, to find that the electric current is and the Z gauge field is a linear superposition of the W³ and Y fields then, when the string terminates, the Y flux cannot terminate because it is a U(1) gauge field and the Y magnetic field is divergenceless. Therefore some field must continue even beyond the end of the string. This has to be the massless field of the theory, that is, the electromagnetic field. In some sense, a finite segment of Z-string terminates on magnetic monopoles The magnetic flux emanating from a monopole is:

This flux may remain frozen-in the surrounding plasma and become a seed for cosmological magnetic fields.

Calculation of the electric field in the vicinity of various geometries of charged bodies

The calculation of electric field in the locale will be determined using the law of Biot-Savart , which explains how the magnetic field do fluctuates with the distance from an electric currenT          

The figure above shows a portion of an electrical circuit carrying a current I .

From the definition of the Biot-Savart it demonstrates the contribution of  at a point K from an elemental section of the electrical circuit having a length of  at a distance r from K, the angle between the current at  and the radius vector from K to  being.

Electromagnetic Field in Presence of Non-trivial Higgs Background

Therefore, from the Biot-Savart Law we are able to understand that,

Where;

₀ = permeability of free space

4rationalization factor

SI units of permeability are T m A^-1 (tesla meters per amp).

From this law we can be able to determine the total magnetic field at any point in the vicinity of the circuit.

Conclusion

The magnetic field on a current curry conductor is directly proportion the current through the conductor and inversely proportion to the perpendicular distance from the conductor to the point where maximum influence of magnetic field is felt (Balanis, 2012, 2-3).

Electric motor on the application of magnetic effect on electric current

An electric motor is a device that converts electrical energy to rotational kinetic energy. Electrical motor consist of a stator that which hold magnetic winding, a rotator that turn, bearing that hold the rotating shaft, a fan that remove heat .

Heat = I² * R * t

Where;

I = current

R = resistance

t = time in seconds

Coil of insulated wire, which is in apposition to turn about a fixed axis, and a strong curved permanent magnet to provide a radial magnetic field.

The current will enter and leave the coil through a split copper called commutator having two halves insulated from each other.

Carbon brushes press lightly against the commutator and are connected to battery terminal.

If the coil is in the horizontal position and the current is switched on, the current flows through the coil, by Fleming’s left hand rule one side of the coil experiences an upward force and the other side will respectively experience a downward force, and since the current in both sides are equal or same then the forces will too be equal and opposite.

The two opposite forces causes the coil to rotate in clockwise direction until it reaches its vertical initial position of sides upward and downward.

In this position the brushes will touch the space between the two halves of the split rings, cutting off current flowing in the coil, consequently, no force acts on the respective opposite sides, but since the coil is in rotation, its momentum carries it past this position and the two split rings will interchange brushes. The direction of current through the coil is reversed and consequently the direction of force on each side of the coil changes. This process is called communitation, the respectively initial sides will interchange in a left right direction, this will automatic influence the forces that will act on the changes of the sides, this will enable the coil to continue rotating in the clockwise direction, so long as the current is flowing through it, the speed of the rotation of the coil increase with the increase in the strength of the current flowing through the coil.

If the terminal of the battery is interchanged, the direction of current will reverse, similarly the direction of the rotation of the coil will also be reversed.

Conclusion

Improvement of on the effectiveness of the motor is done through the following considerations (Kulkarni, Khaparde, 2004, 179-180); first, by winding the coil on a soft iron core, the soft iron core become magnetized and concentrate its magnetic field in the coil, this increases the force on the coil, secondly, increasing the number of turns of the rotation coil, thirdly, by using a stronger magnet and lastly, multiplying the number of coils and commutators  segments.

Reference

Balanis, C. A. (2012). Advance Engineering Electromagnetic. John Wiley. pp, 2-3

Harrington, Roger F. (1961). Harmonic Electromagnetic Fields. McGraw-Hill. pp, 7-8

Kulkarni, S.V. Khaparde, S.A. (2004). Transformer Engineering: Design and practice. CRC press. pp, 179-180.

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https://astrowww.phys.uvic.ca/~tatum/elmag/em06.pdf

https://geosci.uchicago.edu/~moyer/GEOS24705/Readings/ElecReadingII_Motors.pdf