Magnetic Effects of Current & Magnetism

Magnetic Effects of Current & Magnetism


FORCE ON A MOVING CHARGE IN MAGNETIC FIELD

a) A magnetic field is associated only with moving charges & not static.

b) Force on a moving charge in uniform magnetic field is given by, magnitude of force is F_B = Bqv sin


LORENTZ FORCE

• When a charge enters into a region where there are both electric and magnetic fields,
  =
  
  
  MAGNETIC FORCE ON A STRAIGHT CURRENT CARRYING CONDUCTOR
• Force on a straight conductor carrying current in magnetic field is , Magnitude of the force
  F = Bil sin
• Fleming's left hand rule : Stretch the fore-finger, central finger and thumb of left hand mutually perpendicular. Then if the fore finger points in the direction of field () and the central finger in the direction of current (), then thumb will point in the direction of force of direction of motion.
  
  
  Biot-Savart's law :-
• Biot-Savart's law is used to determine the magnetic field at any point due to a current carrying conductor and given as,
  
  B =
  
  Here current element.
  
  
  Ampere's circuital law :-
  "The line integral of around any closed path equals m0I, where I is the total continuous current {steady current} passing through any surface bounded by the closed path.
  
  
  (mathematically)
  
  
  Magnetic Field in Some of the Well Known Cases
• A cylindrical coil of many tightly wound turns of insulated wire with generally diameter of the coil smaller than its length is called a solenoid. Magnetic dipole moment M = i(pR²) n
  Magnetic dipole moment M = i(pR²) n
  
  
  FIELD ON THE AXIS OF A SOLENOID
  
  a) If the point is inside the solenoid of infinite length B =
  
  b) If the solenoid is of infinite length and the point is near one end, B = (here 'n' is number of turns per unit length)
  
  
  FORCE BETWEEN TWO PARALLEL CURRENT CARRYING CONDUCTORS
• When the currents in both the wires are in the same direction, then mutual force between the wires is attractive. When the currents in the wires are in opposite directions, the mutual force between the wires is repulsive.
• Mutual force between the wires is
  Note :- 'l' is the length of the wire that experiences the force.
  
  
  TORQUE ON A CURRENT LOOP IN UNIFORM MAGNETIC FIELD
• When a coil current carrying is placed in a uniform external magnetic field, the net force on it is always zero. Here different parts experience forces in different directions so that the loop may experience a torque or couple.
• A rectangular coil of area A having N turns and carrying current 'i' is placed in a uniform external magnetic field of induction . If 'b' is the angle between the normal to the plane of the coil and the magnetic field, then torque acting on the coil is .
  
  
  MOVING COIL GALVANOMETER
• In MCG, current (i) passing through the coil is directly proportional to its deflection (q)
  NiAB = C
  K is galvanometer constant (C is restoring couple per unit twist)
  Current sensitivity S_V = & Voltage sensitivity
  S_i =
• Cyclotron is a device used to accelerate positively charged particle (like, a-particle, deuterons etc.) to acquire enough energy to carry out nuclear disintegration etc.
• Cyclotron frequency
• Maximum energy of particle : Maximum energy gained by the charged particle
  E_ma =
  Here r₀² is maximum radius of the circular path following by the positive ion.