Dispersion

Here is a complete note on Disperison of light.

Magnetic Material

aBasic concept of Magnetism A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on otherferromagnetic materials, such as iron, and attracts or repels other magnets. Magnetic field: A magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any given point is specified by both a directionand a magnitude (or strength); as such it is a vector field. Magnetic lines of force:The imaginary path in the magnetic field through which unit north pole moves is allowed to do so is called magnetic lines of force. Magnetic lines of force are the lines in the magnetic field , tangent at a point of which shows the direction of Magnetic field at that point.Properties of Magnetic lines of force:1. Magnetic field lines are continuous closed imaginary lines.2. They never intersect each other.3. A tangent drawn at a point in magnetic lines of force show the direction of magnetic field at that point.4. Magnetic lines of force are more crowded where filed is strong and is less crowded at weaker field.5. They are directed from north pole to south pole externally and from south pole to north pole internally in a magnet.Magnetic FluxMagnetic flux ɸ through any surface area in a magnetic field is defined as the number of magnetic lines of force crossing through the surface. Magnetic field intensity:-The strength of a magnetic field at a point is called the magnetic field intensity.The magnetic field intensity at a point defines as the force experienced by a unit North Pole at that point. It is measured in Telsa(T) or Gauss. Intensity of magnetization: It is defined as the net magnetic moment per unit volume of a magnet along the direction of applied magnetic field. It is denoted by I. It is a vector quantity.I= Magnetic moment (M)

Volume (V)=M

VThe unit of I is ampere per meter (Am-1).Magnetic intensity (H): The degree to which a magnetic field can magnetize a material is called magnetic intensity. It is denoted by H. It is a vector quantity. Its unit is ampere per meter (Am-1). It is also called magnetic force. Magnetic intensity magnetize the magnetic substance when placed in this field.H=B

𝜇

What is the difference between Magnetic Intensity and Intensity of Magnetisation? Answer: The magnetic intensity defines the forces that the poles of a magnet experiences in a magnetic field whereas the intensity of magnetization explains the change in the magnetic moment of a magnet per unit volume.

Total magnetic field (B) :

When a magnetic substance is placed in an external magnetic field, it gets magnetized. The resultant magnetic field within the magnetic material is the vector sum of magnetic field due to applied field and the induced magnetic field due to the material itself.Its SI unit is weber m2 or Tesla (T). Its CGS unit is gauss (G)Therefore, total magnetic field B, is written as, B= Applied field (B0)+ magnetic field due to the magnetization of material (BH) i.e. B=B0+BHThe terms B 0 and BH can be expressed into H and I respectively.The strength of applied field due to the magnetic intensity H, B0=𝜇0H and BH=𝜇0I=𝜇0𝜒HWhere, 𝜒 is dimensionless quantity and is known as magnetic susceptibility. The magnetic susceptibility indicates the degree of magnetization of a material in response to an applied magnetic field.Therefore, a

B	=𝜇0H+𝜇0𝛾H
	=𝜇0(1+𝛾)H

Also, in the material medium, total magnetic field B is directly proportional to the magnetic intensity H.i.e. B∝HB=𝜇HWhere, 𝜇 is the absolute permeability of a medium. So, we write, 𝜇=𝜇0(1+𝜒)Magnetic SusceptibilityMagnetic susceptibility of a magnetic substance is the ratio of intensity of magnetization to the magnetic intensity. It is denoted by 𝜒. It has no unit. It is the property of substance.a

∴ 𝜒	= intensity of magnetization (I) magnetic intensity (H)
𝜒	=I H

Magnetic susceptibility 𝜒 measures how much extent the materials can be magnetized. The magnetic materials which can be magnetized strongly, have the value of 𝜒 high positive value. This type of materials are called ferromagnetic materials. The magnetic materials which are weakly magnetized have the value of 𝜒 small positive value. This type of materials are called paramagnetic materials. Likewise, the magnetic materials which are weakly magnetized in the opposite of applied field are called diamagnetic materials. The value of 𝜒 is small negative for these type of materials.Relative PermeabilityAbsolute permeability of a material medium is a measure of the amount of resistance encountered when forming a magnetic field in that medium. It is denoted by 𝜇. If the absolute permeability is taken for the free space (or vacuum), it is denoted by 𝜇0. It is also called the permeability constant. The ratio of absolute permeability of a medium to permeability constant is called relative permeability. It is denoted by 𝜇r. Therefore,Relative permeability (𝜇 r)=𝜇

𝜇0It is a dimensionless quantity. The relation between absolute permeability and magnetic susceptibility is,a

𝜇=𝜇0(1+𝜒)

𝜇 𝜇0=1+𝜒

𝜇r=1+𝜒

Classification of Magnetic MaterialThere are three types of magnetic materials. They are:1. Diamagnetic material2. Paramagnetic material3. Ferromagnetic materialDiamagnetic materialThose substances which are feebly magnetized in the direction opposite to the applied field are called diamagnetic material. Examples of diamagnetic materials are bismuth, copper, water, mercury, alcohol, argon, gold,tin, mercury, antimony etc. The magnetic moment of atoms of a diamagnetic material is zero. They acquire induced dipole moments when the material placed in an external magnetic field. These moments are in opposite in the direction to the applied field.Some properties1. The diamagnetic materials are repelled by magnets.2. When a diamagnetic liquid in a watch glass is placed over two closely spaced pole pieces of the magnet, it is depressed at the middle while in the case of pole pieces separated by a distance, it rises at the middle. Similarly, when a diamagnetic liquid is placed in a U-tube and one of the limbs of the tube is placed between the two strong pole pieces of magnet, the liquid depressed at that limb.3. The diamagnetic materials move from a stronger to a weaker field.4. A diamagnetic rod, freely suspended in a magnetic field, slowly turns to set at right angle to the applied field.5. Since magnetized is opposite in direction to an applied field, the diamagnetic materials have the small value for the intensity of magnetization, I.6. The materials have always negative magnetic susceptibility, and accounts from -10-6 to -10-5.7. These materials are independent of temperature.Paramagnetic MaterialThose materials which are weekly magnetized in the same direction of the applied magnetic field are called paramagnetic material. The examples of paramagnetic materials are aluminum, chromium, oxygen, manganese, alkali, alkaline earth metal etc.The paramagnetic materials have permanent magnetic moments. These moments interacts weekly with each other and randomly orient in the different direction.Some Properties1. The paramagnetic materials are feebly attracted by magnets.2. A paramagnetic rod, freely suspended in a magnetic field, aligns along the field.3. The paramagnetic materials are temperature dependent and follow curve law.4. The relative permeability is nearly unity than ranges from 1.00001 to 1.003 for common ferromagnetic materials at room temperature. So, the magnetic lines of force inside the material placed in a magnetic field are more than that outside it.5. The susceptibility of paramagnetic substances has small positive value.Ferromagnetic MaterialThe ferromagnetic materials are highly magnetized in a magnetic field. The examples of ferromagnetic materials are iron, nickel and cobalt, and their alloys such as alnico. Gadolinium and dysprosium are ferromagnetic at low temperature.Some Properties1. Ferromagnetic materials are highly attracted by magnets.2. Ferromagnetic materials more from weaker to stronger field.3. A ferromagnetic rod, freely suspended in a magnetic field, turns fast to set along the applied field.4. The magnetic susceptibility is positive and very high and varies with applied field.5. The relative permeability is very high in the order of 1000 to 100,000.6. Ferromagnetic dust in a watch glass, placed over two closely spaced pole-pieces of the magnet, increases at the middle, while pole piece is separated by a distance, depresses in the middle.Domain Theory of Ferro Magnetism

Magnetic domain in ferromagnetic material:

Each atom of ferromagnetic substance has a permanent magnetic substance; in the unmagnetised state, the atomic and molecular dipoles are arranged in random so the net magnetic moment is zero. There is a strong interaction with neighboring atoms which keeps their magnetic moment aligned parallel in small regions even in the absence of an external field. These small regions with the volume ranging between 10-12 to 10-8 m3 are called domains. When the material is placed in an external field BO, the domains tend to orient themselves parallel to field B0. As the applied field becomes stronger, the domains, having magnetic moments not aligned with the field, become very small and when the domains fully align to the applied field, the material attains magnetic saturation. On removing the field, the domain walls do not move completely into previous positions. This means material retains a magnetization in the direction of the applied field.HysteresisLagging of magnetic field B behind the magnetic field H in a ferromagnetic material taken through a cycle of magnetization is called the hysteresis.

Hysteresis loop in Ferromagnetic Material:

A ferromagnetic material (iron) is taken and is placed on an external field B0. Now the magnetic field B in the material is studied with the magnetic intensity H ( = B0

𝜇0) is compared. When H is increased the value of magnetic field B increases and reaches maximum value Bs at point A. The value of magnetic field doesnot increases on increase in H. Now lowering the value of H, decreases the magnetic field but doesnot become zero when H is made zero. Value of magnetic field remains BR. (Through AR). H is reversed, then magnetic field continues to decrease and becomes zero at point C. Further increasing the value of H, magnetic field changes its direction and reaches maximum in oppoiste direction at point D. Now again H is decreased and made zero at point E, again reversed the reaches 'F' and ultimately 'A'. The closed loop denotes: a) loss of energy during magnetization b) how strongly is the material magnetizedArea of the hysteresis loop is directly proportional to the elergy loss.The material with broad hysteresis loop with higher retentivity (OR) and coercivity (OC) is suitable for making permanent magnet. Greater area of loop means greater energy has been lost during magnetization thus greater work should be done to demagnetize it. (As in steel)- Suitable for making permanent magnet Less area of loop with low value of coercivity means magnetization can be destroyed easily. ( as in soft iron) - Suitable for making core of transformer.Material with greater value of HC are called magnetically "Hard".

(a) Hysteresis loop in steel (b) Hysteresis loop in soft iron: