Apparatus :

Transformer DC Power Supply Spot Galvanometer Ammeter Three Resistor Boxes Two Switches Reversing KeyIntroduction :When a material is placed in writhing a magnetic field, the magnetic force of the materials electrons will be affected. This affect is known as Faradays law of magnetic induction. However, materials can react quite differently to the presence of an external magnetic field. This reaction is dependent of a number of factors such as the atomic and molecular structure and molecular structure of the material, and the net magnetic field associated with the atoms. The magnetic moments associated with atoms have three origins. These are the electron orbital motion, the change in orbital motion caused by an external magnetic field, and the spin of the electrons.In most atoms electrons occur in pairs. Each electrons in a pair spins in the opposite direction. So when the electrons are pair together, there opposite spins caused there magnetic field to cancel each other. Therefore no magnetic field exists. Alternately, materials with some unpaired electrons will have a net magnetic field and will react more to an external field. Most materials can be classified as ferromagnetic, diamagnetic or paramagnetic.

Diamagnetic materials are slightly repelled by a magnetic field and the material does not retain the magnetic properties when the external field is removed. Diamagnetic materials are solid with all paired electrons and therefore not permanent magnetic moments per atom.

Paramagnetic materials are slightly attached by magnetic field and material does not retain the magnetic properties when the external field is removed. Paramagnetic properties are due to the presence of some unpaired electrons.

Ferromagnetic materials exhibit a strong attraction to magnetic field and are able to retain their magnetic properties after the external field has been removed. Ferromagnetic materials have some unpaired electrons so their atoms have a net magnetic moment. They get there strong magnetic properties due to the presence of magnetic domain. Iron, nickel and cobalt are examples of ferromagnetic materials.Magnetic field strength (H) A magnetic field strength of I ampere/meter is produced at the center of a single circular conductor diameter of 1 m carrying a steady current of 1 A.

Magnetic flux ()The total number of lines of magnetic force in a material is called magnetic flux. The strength of the flux is determined by the number of magnetic domains that are aligned within a material. The total flux is simply the flux density applied over an area. Flux carries the unit of a Weber (Wb), which is simply a Tesla-square meter.Magnetic flux density (B)The number of magnetic lines of fource cutting through a plane of a given area at a right angle is known as the magnetic flux density B. the flux density or magnetic induction has the Tesla as its unit. Tesla is equal to Wb m-2.Magnetization (M)The magnetization is the measure of the extent to which an object is magnetized. It is a measure of the magnetic dipole moment per unite volume of the object. The unite of the magnetization is Am-1.QuantitySymbolSI Unit

FieldHA/m

Flux DensityBTesla

FluxWeber

MagnetizationMA/m

The Hysteresis Loop and Magnetic properties As the current I I figure 1 increases from Zero, the magnetization M will increase from zero up to a certain value at which all the domains in the iron are perfectly aligned. Any feather increases in i will have no effect on the value of M , and the iron is said to be saturated. A curve of the total field B vs. the applied field H, as H increases from zero is called a magnetization curve. A typical magnetization curve for iron is given in figure 2.Suppose we reach some arbitrary points (H0 ,B0) on the magnetization cure shown (dotted) in figure 3.if we then decreases H to zero (by decreasing the current in the external coil),the iron will remain partly magnetized and there will be a residual field BR, by reversing the current, we can decreases B to zero at a value of H known as the coercive force, Hc As H is made more negative, the iron magnetizes in the reverse directions and it will arrive at the point (-H0,-B0) when the reverse current is equal in magnitude to the initial to the initial forward current. A curve of B Vs H for a complete cycle of increasing and decreasing current is known as hysteresis curve. Various hysteresis curves are possible for a given specimen of iron, depending at which point on the magnetization curve the hysteresis curve is started.

Basic relations of magnetic Hysteresis theoryRetentivity -A measure of the residual flux density corresponding to the saturation induction of a magnetic material. In other words it is materials ability to reatain a certain amount of residual magnetic field when the magnetizing fore is removed after achieving saturation.( The value of B at point BR on the hysteresis curve.)Coercive force-The amount of reverse magnetic field which must applied to a megnatic material to make the magnetic flux return to zero .(the value of H at point -Hc on the hysteresis curve.)Permeability-Permeability is a material property thet describe the case with which a magnetic flux is established in a material.it is the ration of the flux density to the magnetic force and , therefore present by the following equation:=B/Hit is clear that the equation describe the slope of the curve at any point on the hysteresis curve. The permeability value given in papers and reference meterials is usually the maximum permeability or the maximum relative permeability. The maximum permeability is the point where the slope of the B-H curve unmagnified materials is the greatest. This point often take as the point where a straight line from the origin is tangent to the B-H curve.The relative permeability is found by taking the ration of the materials permeability to the permeability in free space

Theory and Diagrams :

if we wind a coil of N turns on an iron ring and passes a current I through the coil, then the value of H in the iron can be found from Ampheres law , giving

Where l is the length of the iron ring, the value of H is proportional to I and N but does not depend on the state of magnetization of the iron.If is the flux produced by given current in the ring, and there are n windings in the secondary coil, then quantity of the charge set in the motion in the secondary when this flux created or destroyed is n /R , R being the total resident of the secondary coil.

When this charge is passes through a spot galvanometer, we have

When, K is the galvanometer constant and d is the galvanometer deflection in mm . But

Where A is the area of the cross section of the ring. There fore

The power dissipated in the transformer at the given frequency is,

The power used in the primery , p = vi, where v = N A (dB/dt) and I = H l/NThere fore

Volume of the iron core and is the area enclosed by the hysteresis curve.Therefore , power = (Area of curve) (Volume of iron)Procedure :

1) The spot Galvanometer was placed 1meter far from the scale and it was adjusted to zero.

2) The apparatus was fixed as shown in the figure 4.3) S1 opened and S2 closed; primary current was varied using R2 resistor, measured the input current i (in A) and the galvanometer deflection d with decreasing the primary resistance. After every current increases the coil must be de magnetized.

4) S1 and S2 was closed and adjusted R1 till the supply current become saturation value.5) r was adjusted to obtain the maximum deflection of the light spot on scale.6) The input current and the galvanometer deflection d was measured. (+) sign was used to measure both current and deflection. 7) Then the current was reversed by using the reversible key and got the deflection corresponding to reverse maximum current.

8) Again returned to the positive saturation current and S2 was opened, that reduces i to zero. Once again the spot galvanometer deflection was measured.

9) The input current was reduced from its previous value by using the R2 and spot galvanometer deflection was measured corresponding to the input current.

10) This was repeated until input current reach its reverse maximum value and measured input current and corresponding galvanometer deflection in mm and it was recorded in a table.

11) Secondary coil resistance and resistance of the galvanometer was measured.

Calculations :Cross sectional area of the iron core is

Length of the iron core is

Round off value for Graph 01Deviation( 10 -2 m)Current (A)B (Tesla) 1010H (A/m)

0.40.10.20105

0.50.20.25210

4.60.32.26315

6.80.43.34420

10.30.55.05525

11.20.65.50630

13.60.76.67735

13.90.86.82840

15.60.97.65945

15.51.07.611049

17.01.18.341154

17.01.28.341259

18.01.38.831364

18.21.48.931469

19.01.59.321574

18.91.69.271679

19.91.79.761784

19.61.89.621889

20.31.99.961994

20.02.09.812099

Gradient of the Graph

Round off value for Graph 02Current(A)d1+10-2d2+10-2d1-10-2d2-10-2B11010B21010B31010B41010H

1.320.621.90.522.612.01.2-12.0-0.91385

0.901.219.40.819.911.72.2-11.9-2.1945

0.731.517.91.412.011.52.7-11.6-5.7766

0.591.615.91.516.011.53.7-11.5-3.7619

0.511.814.61.814.511.44.2-11.4-4.3535

0.432.012.91.812.711.35.0-11.4-5.2451

0.392.210.72.010.711.25.9-11.3-6.0409

0.342.48.92.49.011.16.7-11.1-6.7357

0.312.56.42.46.411.07.9-11.1-7.9325

0.282.65.62.65.411.08.2-11.0-8.3294

0.242.74.02.64.010.99.0-11.0-9.0252

0.203.13.12.93.010.79.2-10.8-9.4210

0.153.22.13.22.010.79.7-10.7-9.7157

0.103.61.53.31.410.59.8-10.6-10.0105

0.053.90.83.80.510.410.0-10.4-10.252

0.003.90.23.90.010.410.3-10.4-10.40

Area of the Graph is = 141 1 2501010 = 3.51010 T A.m-1Power = (Area of the curve)(Volume of iron) = 3.51010 2.379710-5 = 8.3289105 W

Conclusion :Relative permeability of iron = Area of the hysteresis curve = 3.51010 TAm-1Volume of iron core = 2.379710-5 m3Power= 8.3289105 W

Questions :

1. To check the power loss of a transformer, measure the voltage and current at the input and output. Then multiply the voltage times the current of each to find the watts. Subtract the output wattage from the input. The difference equals the power dissipated.

Wire ResistanceThe coils of a transformer, made from long pieces of wire, have resistance which acts like any load on electrical current. The coils of the wire heat up while the transformer operates, using some of its power.

Induction LossesThe primary winding of a transformer induces current into the secondary winding around a magnetic core. The core itself resists the induction process slightly, causing a loss of power.

3 We use 50Hz frequency because our main current has 50Hz. And also when increase the frequency it may make more power dissipation.

Discussion :Ferromagnetic and ferrimagnetic materials have non-linear initial magnetisation curves. It is on the dotted lines in figure, as the changing magnetisation with applied field is due to a change in the magnetic domain structure. These materials also show hysteresis and the magnetisation does not return to zero after the application of a magnetic field. Figure shows a typical hysteresis loop; the two loops represent the same data, however, the red loop is the polarisation and the blue loop the induction, both plotted against the applied field.

A typical hysteresis loop for a ferro- or ferri- magnetic material.

The first quadrant of the loop is the initial magnetisation curve (dotted line), which shows the increase in polarisation and induction on the application of a field to an unmagnetised sample. In the first quadrant the polarisation and applied field are both positive, that is they are in the same direction.

The polarisation increases initially by the growth of favourably oriented domains, which will be magnetised in the easy direction of the crystal. When the polarisation can increase no further by the growth of domains, the direction of magnetisation of the domains then rotates away from the easy axis to align with the field. When all of the domains have fully aligned with the applied field saturation is reached and the polarisation can increase no further.

If the field is removed the polarisation returns along the solid red line to the y-axis (i.e. H=0), and the domains will return to their easy direction of magnetisation, resulting in a decrease in polarisation. In the figure, the line from the saturation point to the y-axis is horizontal, which is representative of a well aligned material, where the domains are magnetised in the easy direction of the crystal at the saturation point.

If the direction of applied field is reversed that mean in the negative direction, then the polarisation will follow the red line into the second quadrant. The hysteresis means that the polarisation lags behind the applied field and will not immediately switch direction into the third quadrant .

After applying a high enough field saturation polarisation will be achieved in the negative direction. If the applied field is then decreased and again applied in the positive direction then the full hysteresis loop is plotted.

If the field is repeatedly switched from positive to negative directions and is of sufficient magnitude then the polarisation and induction will cycle around the hysteresis loop in an anti-clockwise direction. The area contained within the loop indicates the amount of energy absorbed by the material during each cycle of the hysteresis loop.