Chapter 5. Magnetism and Matter

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Peter Stuart Manning
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1 Chapter 5 Magnetism and Matter TABLE 5.1 THE DIPOLE ANALO Diamagnetic materials, when placed in a magnetic field, are magnetized in the direction opposite to the magnetic field; whereas paramagnetic and ferro-magnetic materials are magnetized in the same direction as that of the magnetic field. A wire of length L metre carrying a current I ampere is bent into a circle, the magnitude of its magnetic moment in M.K.S. unit is I L 2 /4 π When a bar magnet of dipole moment m is place in a uniform magnetic field B, The force on it is zero, The torque on it is m x B, Its potential energy is m.b, perpendicular to B. where we choose the zero of energy at the orientation when m is Permeability (µ) The permeability is defined as the ratio of magnetic induction (B) to the magnetizing force (H), i.e., µ = B/H

2 Consider a bar magnet of size l and magnetic moment m, at a distance r from its mid-point, where r >> l, the magnetic field B due to this bar is, = (along axis) = - (along equator) Gauss s law for magnetism states that the net magnetic flux through any closed surface is zero φ B = B. S=0 allare elemen In a hydrogen atom, the electron moves in an orbit of radius 0 5 Å making revolution per second. The magnetic moment associated with the orbital motion of the electron is ampere-meter 2. The earth s magnetic field resembles that of a (hypothetical) magnetic dipole located at the centre of the earth. The pole near the geographic north pole of the earth is called the north magnetic pole. Similarly, the pole near the geographic South Pole is called the south magnetic pole. This dipole is aligned making al small angle with the rotation axis of the earth. The magnitude of the field on the earth s surface 4 x 10-5 T. The magnetic susceptibility of a paramagnetic material charges inversely as the absolute temperature. The angle of dip at magnetic pole of the carth is 90 0 and at the equator is zero. Susceptibility (χ) The susceptibility is defined as the ratio of the intensity of magnetization (I m ) to the magnetizing field (H) in which he material is placed, i.e., χ = ( I m /H )

3 Three quantities are needed to specify the magnetic field of the earth on its surface the horizontal component, the magnetic declination, and the magnetic dip. These are known as the elements of the earth s magnetic field. Intensity of Magnetic Field (H) The intensity of magnetic field is defined as the force experienced by a unit North Pole placed at a point in the field. In M.K.S. system, the unit of H is Amp. Turn/metre. The direction of H is the same as the direction of B and is related as B = µ H Where µ is called the magnetic permeability. Consider a material place in a external magnetic field B 0. The magnetic intensity id defined as, = The magnetization M of the material is its dipole moment per unit volume. The magnetic field B in the material is, B = µ (H + M) Magnetization and demagnetization of soft iron is easier as compared to steel. The unit of magnetic dipole moment is mapere-meter 2. For a linear material M = χ H. So that B = µ H and χ is called the magnetic susceptibility of the material. The three quantities, χ, the relative magnetic permeability µ r, and the magnetic permeability µ are related as follows: µ = µ 0 µ r µ r = 1 + χ

4 Magnetic materials are broadly classified as: diamagnetic, paramagnetic, and ferromagnetic, for diamagnetic materials χ is negative and small and for paramagnetic materials it is positive and small. Ferromagnetic materials have large χ and are characterized by non-linear relation between B and H. they show the property of hysteresis. Substances, which at room temperature, retain their ferromagnetic property for a long period of time are called permanent magnets. A consequence of the fact that magnetic monopoles do not exist is that the magnetic field lines are continuous and form closed loops. In contrast the electrostatic lines of force begin on a positive charge and terminate on the negative charge (or fade out at infinity). He earth s magnetic field is not die to a huge bar magnet inside it. The earth s core is hot and molten. Perhaps convective currents in this core are responsible for the earth s magnetic field. As to what dynamo effect sustains this current, and why the earth s field reverses polarity every million years or so we do not know. There exists a perfect diamagnet, a superconductor. This is a metal at very low temperatures. In this case χ = - 1, µ r = 0, µ = 0. The external magnetic field is totally expelled. Interestingly, this material is also a perfect conductor. However, there exists no classical theory which ties these two properties together. A quantum-mechanical theory by Bardeen, cooper and Schrieffer (BCS theory) explains these effects. Diamagnetism is universal. It is present in all materials. But it is weak and hard to detect if the substance is para-or ferromagnetic.

5 Intensity of Magnetization (I m ), When a magnetic material is placed in a magnetic field, it is magnetized. Now it acquires magnetic moment M. the intensity of magnetization is defined as the magnetic moment per unit volume, i.e., = =.. = Where a is the area of cross-section of the material. So the intensity of magnetization may also be defined as pole strength (m) per unit area of crosssection (a). Magnetic induction or Flux Density (B) The flux density is the total number of lines of force per unit area due to the flux density B 0 in vacuum produced by that magnetizing field and flux density B m due to the magnetization of the material. Thus B = B 0 + B m. The unit of B is weber/metre 2. Electro-magnets are made of soft iron because soft iron has large permeability and large retentivity. Dipole moment Equatorial Field for a short dipole Axial Field for a short dipole External Field: torque External Field: Energy Electrostatics 1/ε 0 p -p/4πε 0 r 3 2p/4πε 0 r 3 p E -p.e Magnetism µ0 m -µ0m / 4πr3 µ0 2m / 4πr3 M B -m. B

6 MAGNETIC SUSCEPTIBILITY OF SOME ELEMENTS AT 300 K Diamagnetic substance % Paramagnetic substance χ Bismuth x 10-5 Aluminium 2.3 x 10-5 Copper -9.8 x 10-6 Calcium 1.9 x 10-5 Diamond -2.2 x 10-5 Chromium 2.7 x 10-4 Gold -3.6 x 10-5 Lithium 2.1 x 10-5 Lead -1.7 x 10-5 Magnesium 1.2 x 10-5 Mercury -2.9 x 10-5 Niobium 2.6 x 10-5 Nitrogen (STP) -5.0 x 10-9 Oxygen (STP) 2.1 x 10-6 Silver -2.6 x 10-5 Platinum 2.9 x 10-4 Silicon -4.2 x 10-6 Tungsten 6.8 x 10-5 Physical quantity Symbol Nature Dimension Units Remarks Permeability of free space Magnetic field, Magnetic induction, Magnetic flux density µ 0 Scalar [MLT -2 A -2 ] T m A -1 µ0/4π = 10-7 B Vector [MT -2 A -1 ] T (tesla) 10 4 G (auss) = 1 T Magnetic moment m Vector [L -2 A] A m 2 Magnetic flux φ B Scalar [ML 2 T -2 A -1 ] W (weber) W = T m 2 Magnetization M Vector [L -1 A] A m -1 Magnetic moment Volume

7 Magnetic intensity H Vector [L -1 A] A m -1 B = µ 0 (H + M) Magnetic strength field Magnetic susceptibility Relative permeability Magnetic permeability magnetic χ Scalar - - M = χh µ r Scalar - - B = µ 0 µ r H µ Scalar [MLT -2 A -2 ] T m A -1 µ = µ 0 µ r NA -2 B = µh THANK YOU

Current Loop as a Magnetic Dipole & Dipole Moment:

MAGNETISM 1. Bar Magnet and its properties 2. Current Loop as a Magnetic Dipole and Dipole Moment 3. Current Solenoid equivalent to Bar Magnet 4. Bar Magnet and it Dipole Moment 5. Coulomb s Law in Magnetism