Magnetism

Magnetism

• POLE STRENGTH :
• Pole strength is a scalar and its SI units is ampere meter Dimensional formula [m] = [AL ]
• It depends on (a) nature of the material of the magnet (b) level of magnetisation (c) directly proportional to area of cross section.
• Pole strength is independent of the shape of the magnet.
  
• MAGNETIC MOMENT :
• It is measured as the product of length and pole strength M = 2 l x m.
• Its S.I unit is ampere - metre²or N - m / Tesla or N - m³/ weber [M] = [IL²].
• It is a vector with its direction from south pole to north pole along its axial line.
• M = I × V or M =
  I Intensity of magnetisation V magnetised volume, C moment of the couple.
  Note:- When a thin bar magnet of magnetic moment 'M' and length '2l' is bent at its mid point with an angle '' between the two parts, its new magnetic moment M¹= M sin (/2).
  
  
• COULOMB'S INVERSE SQUARE LAW :
• The force between two isolated magnetic poles is expressed by
• F =
  
• MAGNETIC INDUCTION OR INDUCTION FIELD STRENGTH OR MAGNETIC FLUX DENSITY :
• It is numerically equal to the force experienced by unit north pole kept at the given point
  a) 'B' is a vector having direction in the direction of auxilary field H.
  b) Dimensional formula [B] = = [MT^-2A^-1].
  c) S.I unit weber / m²or N/A - m or tesla
  d) 1 tesla = 10⁴gauss
• Magnetic induction due to an isolated pole of strength 'm' is given by B = in air, away from pole of it is N-pole & towards the pole if it is S-pole
• Magnetic flux per unit area is called magnetic induction of flux density B = .
  
• INTENSITY OF THE MAGNETIC FIELD OR MAGNETISING FIELD STRENGTH (H) :
  
  a) 'H' is an auxilary field which is measured as the ratio of magnetic induction to the permeability of the medium at the given point
  b) H = (in medium) and H = in air or vacuum
  c) H is a vector in the direction of the force.
  d) I.M.F = [H] = [AL^-1]
  e) S.I unit of H is Am^-1
• MAGNETIC FLUX :
• The total number of magnetic lines of induction passing normal to the given cross section is called magnetic flux. It is measured as the dot product of magnetic induction and areal vector .
  = BA cos
  is the angle made by magnetic induction with the normal to the area
  a) It is a scalar
  b) S.I unit of flux weber
  c) 1 weber = 10⁸maxwell
  
• TORQUE ACTING ON A BAR MAGNET IN A UNIFORM MAGNETIC FIELD.
• When a magnet with magnetic moment M is suspended in a uniform field of induction B at an angle q with the field direction then the couple acting on the magnet.
  C = MB sin and vectorially
• When = 90°is maximum C_max= MB
  If = 90°and B = 1, C_max= M
• When = 0° C = 0
  
• FIELD ON AXIAL LINE :
• B at any point on the axial line of a bar magnet is
  C =
• In case of short bar magnet l < < d B =
• Direction to is from S to N along the axial line.
• Two magnets of different lengths having same moment are taken. Magnetic field at distance 'd' from the centre on the axial line is more of the longer magnet.
  
  
• DEFLECTION MAGNETOMETER :
  
  1. Deflection magnetometer works on the principle of tangent law
  2. Tangent law B = B_Htan
  B = Magnetic field due to bar magnet.
  = horizontal component of earth's magnetic field.
  = the angle through the needle deflects.
  
• VIBRATION MAGNETOMETER :
• It works on the principle that when a bar magnet is suspended freely in a uniform magnetic field and is displaced from its equilibrium, it starts vibrating and executes SHM about the equilibrium position.
• The plane mirror with the index line helps to count the vibrations of the magnet and avoids the error due to parallax.
  3. The time period of vibrating T = where is the moment of inertia of the bar magnet about the axis of oscillation.
  m = mass of the magnet
  l = length of the magnet
  b = breadth of the magnet
  = horizontal component of earth's magnetic field
  
• Magnetic Properties of Matter
  Atom As A Magnetic Dipole
  We now derive an expression for the magnetic dipole moment due to orbital motion of electron figure below shows an electron revolving in an orbit of radius r with an angular velocity w. The circulating electron is equivalent to a single-turn current loop. The magnetic dipole moment of this current loop is given by;
  
  M = iA
  Now
  
  M = iA = ...(i)
• According to Bohr's theory, the angular momentum of an electron (mvr) in a stationary orbit can have only those values which are integral multiples in h/2p, i.e.
  ..(ii)
  where n = 1, 2, 3, ....
  From (i) and (ii)
  
  or
  The least value of the magnetic dipole moment of an electron due to orbital motion occurs when n = 1. This is called Bohr magneton and is represented by m_b.
  M = n _B where
  
  
  CURIE LAW
• According to Curie law, for away from saturation the magnetic susceptibility of a paramagnetic substance is inversely proportional to absolute temperature.
  ...(1)
  
  when a ferromagnetic material is heated, it becomes paramagnetic at a certain temperature. This temperature is called curie point or curie temperature (Tc). For ferromagnetic substance we have, C is called Curie constant.
  
  
  TC= Curie point
  T (> T_C) = temperature above curie point.
  C' = Another Curie Constant
  The Curie point of iron is 1043 K.