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What are magnetic properties of matter

• All substances possess magnetic properties and most general definition of magnetism defines it as a particular form of interactions originating between moving electrically charged particles.
• Magnetic interaction relates spatially separate material objects and it is transmitted by means of magnetic field about which we have already studied .This magnetic field is important characteristics of EM form of matter.
• We already know that source of magnetic field is a moving electric charge i.e. an electric current. On atomic scale, there are two types of macroscopic current associated with electrons.
a) Orbital current is which electron in an atom moves about the nucleus in closed paths constituting electric currents loops
b) Spin currents related to the internal degrees of freedom of the motion of electrons and this can only be understood through quantum mechanics.
• Like electrons in an atom, atomic nucleus may also have magnetic properties like magnetic moment but it is fairly smaller then that of electrons.
• Magnetic moment m is nothing but the quantitative measure of the magnetism of a particle.
• For an elementary closed loop with a current i in it, the magnitude |m| of a magnetic moment vector equals the current times the loop area S i.e.
|m|=iS and direction of m can be determined using right hand rule.
• All micro structural elements of matter electrons, protons and neutrons are elementary carriers of magnetic moment and combination of these can be principle sources of magnetism
• Thus magnetic properties are inherent to all the substances i.e. they are all magnets
• An external magnetic field has an influence on these atomic orbital and spin currents and two basic effects of an external field are observed
i) First is diamagnetic effect which is consequences of faraday's law of induction. According to the Lenz law’s, a magnetic field always sets up an induced current with its magnetic field direction opposite to an initial field .Therefore diamagnetic moment created by the external field is always negative related to this field
ii) Second effect occurs if there is a resultant non zero magnetic moment in the atom i.e. there is a spin magnetic moment and orbital magnetic moment .In this case external field will attempt to orient the intrinsic atomic magnetic moment in its own direction .As a result a positive moment parallel to the field is created and this is called paramagnetic moment.
• Because of the universality of the diamagnetic effect, all substances possess diamagnetic.
• However, diamagnetism is by no means actually observed in all matter. This is because in many instances the diamagnetic effect is masked by the more powerful paramagnetic effect.
• Thus in paramagnetic substances we actually always observe a difference effect produced by the prominent Para magnetism and weaker diamagnetism.
• Polarization (quick review)

Longitudinal wave- has the same property with respect to any plane through its line of polarization.
Transverse waves- behaves differently in different planes. Light waves are transverse in nature and the viberation in them are at right angles to the direction in which wave is traveling.
Plane Polarized - Since the viberations constituting the beam of light are confined only to one definite plane through the axis of the beam, the light is generally said to be plane polarized. Properties of plane polarized light beam wrt two planes, one containing the viberation and other at right angles to it

Note that
• Vibrations of polarized light are linear --- light is plane polarized
• Vibrations of polarized light are circular --- light is circularly polarized
• Vibrations of polarized light are elliptic --- light is elliptically polarized
• circular and elliptical vibrations are the resultant of two linear vibrations perpandicular to each other differing in phase by π/2.
Polarization by reflection
• It is the simplest method of obtaining plane polarized light.
• This method was first discovered by Etiennie Louis Malus.
• When a beam of light is reflected from the surface of a transparent medium the reflected light is partially polarized and the degree of polarization varies with the angle of incidence.
• Percentage of polarized light in reflected beam is greatest when it is incident at an angle known as angle of polarization for the medium which is equal to 57.5 degree for glass and varies slightly with the wavelength of incident light.
• Complete polarization is possible only with monochromatic light.
• Reflected light is said to be plane polarized in the plane of incident.
Brewster's Law
• This Law states that there is a simple relation between the angle of maximum polarization and the refractive index of the medium. This relation known as Brewster's Law is given by
μ=tan i
where i is the angle of incidence
and μ is the index of refraction
• Using this law it can be showen that 'when light is incident at angle of maximum polarization the reflected ray is at right angles to the refracted ray. From Brewster's Law
μ=tan i = (sin i)/(cos i)
From Snell's Law
μ = (sin i)/(sin r)
where r is the angle of refraction
Therefore , (sin i)/(cos i) = (sin i)/(sin r)
(sin i)/(sin (90- i)) = (sin i)/(sin r)
or we have
90-i=r
this gives i+r=90 degree
showing that at maximum angle of polarization reflected and refracted rays are at right angles.
• Brewster's Law is obeyed even when light is reflected at the surface of rarer medium.
• Light reflected from both the upper and lower surfaces of a glass plate will be polarized in the plane of incidence.
Double Refraction

• Certain crystals split a ray of incident light into two refracted rays , one which gives the fixed image and follows all the laws of refraction and this ray is known as ordinary ray (o ray). Other ray gives an image that rotates with rotation of crystal and this ray is know as extra ordinary ray (e ray).
• Both e and o rays are plane polarized.
• When the crystal is rotated about the incident ray as an axis , the o-ray remains fixed but the e-ray revolves around it.
• The index of refraction for e-ray is therefore a function of direction.
• There is always one direction in the crystal for which there is no distinction between the o and e rays and this direction is called optic axis.
• e ray and o ray are parallel to each other.
• Plane of polarization of both e and o rays are at right angles to each other.
• A class of crystals in which there is a single direction known as optic axis along which all waves are transmitted with one uniform velocities while in any other direction there are two velocities are called uni-axial crystals for example calcite and tourmaline crystals are uni-axial.
• Crystals having two optical axis that is they have two directions of uniform velocity are bi-axial crystals for example topaz, mica etc.
Law of Malus
• Intensity of incident polarized ray is equal to the sum of the intensities of two refracted rays
Io = a2sin2θ
and , Ie = a2cos2θ
Io+Ie=a2=I

Comparison between mechanical energy of mass spring system and electrical LC circuit

Table given below compares the mechanic oscillations of mass spring system with that of electrical oscillations in an L-C circuit

What is a magnetic field

• We all ready know that a stationery charges gets up a electric field E in the space surrounding it and this electric field exerts a force F=q0E on the test charge q0 placed in magnetic field.
• Similarly we can describe the intraction of moving charges that, a moving charge excert a magnetic field in the space surrounding it and this magnetic field exert a force on the moving charge.
• Like electric field, magntic field is also a vector quantity and is represented by symbol B
• Like electric field force which depend on the magnitude of charge and electric field, magnetic force is propotional to the magnitude of charge and the strength of magnetic field.
• Apart from its dependence on magnitude of charge and magnetic field strength magnetic force also depends on velocity of the particle.
• The magnitude magnetic force increase with increase in speed of charged particle.
• Direction of magnetic force depends on direction of magnetc field B and velocity v of the chared particle.
• The direction of magnetic force is not alonge the direction of magnetic field but direction of force is always perpendicular to direction of both magnetic field B and velocity v
• Test charge of magnitude q0 is moving with velocity v through a point P in magnetic field B experience a deflecting force F defined by a equation
F=qv X B
• As mentioned earlier this force on charged particle is perpendicular to the plane formed by v and B and its direction is determined right hand thumb rule.

• When moving charge is positive the direction of force F is the direction of advance of hand screw whose axis is perpendicular to the plane formed by v and B.

• Direction of force would be opposit to the direction of advance screw for negative charge moving in same direction.
• Magnitude of force on charged particle is
F=q0vBsinθ
where θ is the angle between v and B.
• If v and B are at right angle to each other i.e. θ=90 then force acting on the particle would be maximum and is given by
Fmax=q0vB                   ----(3)
• When θ=180 or θ=0 i.e. v is parallel or antiparallel to B then froce acting on the particle would be zero.
• Again from equation 2 if the velocity of the palticle in the magnetic field is zero i.e., particle is stationery in magnetic field then it does not experience any force.
• SI unit of strength of magnetic field is tesla (T). It can be defined as follows
B=F/qvsinθ
for F=1N,q=1C and v=1m/s and θ=90
1T=1NA-1m-1
Thus if a charge of 1C when moving with velocity of 1m/s along the direction perpendicular to the magnetic field experiences a force of 1N then magnitude of field at that point is equal to 1 tesla (1T).
• Another SI unit of magnetic field is weber/m2 Thus
1 Wb-m-2=1T=1NA-1m-1
In CGS system, the magnetic field is expressed in 'gauss'. And 1T= 104 gauss. Dimention formula of magnetic field (B) is [MT-2A-1]
For full chapter visit physicscatalyst.com

Heating Effects of current (Concept Map)

For reading complete chapter on this topic visit Thermal effects of currents

Escape Velocity

• Escape velocity is the minimum velocity that should be given to the body to enable it to escape from the gravitational field of the earth .
• The energy given to the body to project it with the escape velocity is called escape energy.
• Escape velocity of earth is 11.2Km/sec
• Valve of escape velocity does not depend on the mass of the projected body of, instead it depends on the mass and radius of the planet from which it is being projected.
• There are no atmsphere on the planets where root mean square velocity is more than the escape velocity.
• The value of escape velocity does not depend on the angle and direction of projection instead depends on density, mass and acceleration due to gravity of the planet.

How to use Gauss's Law to find electric field

We all know that Gauss's law is basically the relation between the charge distribution producing the electrostatic field to the behaviour of electrostatic field in space. Also Gauss's law is based on the fact that flux through any closed surface is a measure of total amount of charge inside that surface and any charge outside that surface would not contribute anything to the total flux. Now we'll go through the main steps which we can employ for applying Gauss's Law

1. First identify the symmetry properties of the charge distribution. By this we mean that the point at which the field is to be determined must lie on a surface and this surface must have enough symmetry which allows integrals involved to be evaluated properly.
2. Determine the direction of the electric field and a surface on which the magnitude of electric field is constant.
3. Now choose the Gaussian surface accordingly for example if the problem has spherical symmetry then Gaussian surface would usually be spherical and for cylindrical symmetry problem Gaussian surface would be cylindrical.
4. Calculate the flux through the Gaussian surface.
5. Now calculate the charge enclosed inside the chosen Gaussian surface.
6. Equate the two sides of Gauss's law in order  to find the expression for the magnitude of the electric field in that region of space.

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