Magnetic Field

1
Magnetic Field

• A magnetic field is a region in which a body with
  magnetic properties experiences a force.

2
Sources of Magnetic Field

• Magnetic fields are produced by electric
  currents, which can be macroscopic currents in
  wires, or microscope currents associated with
  electrons in atomic orbits.

3
Magnetic Field Lines

• A magnetic field is visualised using magnetic
  lines of force which are imaginary lines such
  that the tangent at any point gives the direction
  of the magnetic field at that point.

4
Magnetic Flux Pattern
5
The Earths Magnetic Field

• The Earth's magnetic field appears to come from a
  giant bar magnet, but with its south pole located
  up near the Earth's north pole.

6
Properties of Magnetic Field Lines

• Magnetic lines of force never intersect.
• By convention, magnetic lines of force point from
  north to south outside a magnet (and from south
  to north inside a magnet).
• Field lines converge where the magnetic force is
  strong, and spread out where it is weak. (Number
  of lines per unit area is proportional to the
  magnetic field strength.)

7
Magnetic flux pattern due to current in a
straight wire at right angles to a uniform field
Net flux is greater on this side of the wire
Net flux is lesser on this side of the wire
8
Flemings Left Hand Rule

• If you point your left forefinger in the
  direction of the magnetic field, and your second
  finger in the direction of the current flow, then
  your thumb will point naturally in the direction
  of the resulting force!

9
Force on a current-carrying conductor

• The direction of magnetic force always
  perpendicular to the direction of the magnetic
  field and the direction of current passing
  through the conductor.

10
Magnetic Flux Density

• The magnetic flux density is defined as the force
  per unit length per unit current acting on a
  current-carrying conductor at right angle to the
  field lines.

Unit tesla (T) or gauss (G), 1 G
10-4 T or weber/m2
11
Typical Values of the magnetic flux density
12
Magnetic Field Measurements

• Using a current balance (d.c.)
• Using a search coil (a.c.)
• Using a Hall probe (d.c.)

13
Magnetic flux density due to a straight wire

• Experiments show that the magnetic flux density
  at a point near a long straight wire is

r
P ?

• TThis relationship is valid as long as r, the
  perpendicular distance to the wire, is much less
  than the distance to the ends of the wire.

14
Calculation of B near a wire
Where ?o is called the permeability of free
space.
Permeability is a measure of the effect of a
material on the magnetic field by the material.
15
Magnetic Field due to a Solenoid

• The magnetic field is strongest at the centre of
  the solenoid and becomes weaker outside.

16
Magnetic Flux Density due to a Solenoid

• Experiments show that the magnetic flux density
  inside a solenoid is

and
So we have
or
where
17
Variation of magnetic flux density along the axis
of a solenoid

• B is independent of the shape or area of the
  cross-section of the solenoid.
• At a point at the end of the solenoid,

18
Magnetic Flux Density due to Some
Current-carrying conductors(1)

• Circular coil

• Helmholtz coils

19
Magnetic Flux density due to Some
Current-carrying Conductors (2)
20
Force on a moving charge in a magnetic field

• The force on a moving charge is proportional to
  the component of the magnetic field perpendicular
  to the direction of the velocity of the charge
  and is in a direction perpendicular to both the
  velocity and the field.

http//webphysics.davidson.edu/physlet_resources/b
u_semester2/c12_force.html
21
Right Hand Rule

• Direction of force on a positive charge given by
  the right hand rule.

22
Free Charging Moving in a Uniform Magnetic Field

• If the motion is exactly at right angles to a
  uniform field, the path is turned into a circle.

• In general, with the motion inclined to the
  field, the path is helix round the lines of
  force.

23
Mass Spectrometer

• The mass spectrometer is used to measure the
  masses of atoms.

• Ions will follow a straight line path in this
  region.

• Ions follow a circular path in this region.

24
Aurora Borealis (Northern Lights)

• Charged ions approach the Earth from the Sun (the
  solar wind and are drawn toward the poles,
  sometimes causing a phenomenon called the aurora
  borealis.

25
Causes of Aurora Borealis

• The charged particles from the sun approaching
  the Earth are captured by the magnetic field of
  the Earth.
• Such particles follow the field lines toward the
  poles.
• The high concentration of charged particles
  ionizes the air and recombining of electrons with
  atoms emits light.

http//www.exploratorium.edu/learning_studio/auror
as/selfguide1.html
26
Hall Effect

• When a current carrying conductor is held firmly
  in a magnetic field, the field exerts a sideways
  force on the charges moving in the conductor.
• A buildup of charge at the sides of the conductor
  produces a measurable voltage between the two
  sides of the conductor.

• The presence of this measurable transverse
  voltage is called the Hall effect.

27
Hall Voltage

• The transverse voltage builds up until the
  electric field it produces exerts an electric
  force on the moving charges that equal and
  opposite to the magnetic force.
• The transverse voltage produced is called the
  Hall voltage.

28
Charge Carriers in the Hall Effect

• The Hall voltage has a different polarity for
  positive and negative charge carriers.
• That is, the Hall voltage can reveal the sign of
  the charge carriers.

29
Hall Probe

• Basically the Hall probe is a small piece of
  semiconductor layer.

• Four leads are connected to the midpoints of
  opposite sides.

• When control current IC is flowing through the
  semiconductor and magnetic field B is applied,
  the resultant Hall voltage VH can be measured on
  the sides of the layer.

30
Force between two parallel current-carrying
straight wires (1)

• Parallel wires with current flowing in the same
  direction, attract each other.
• Parallel wires with current flowing in the
  opposite direction, repel each other.

31
Force between two parallel current-carrying
straight wires (2)

• Note that the force exerted on I2 by I1 is equal
  but opposite to the force exerted on I1 by I2.

32
Definition of the ampere

• The ampere is the constant current which, if
  maintained in two parallel conductors of infinite
  length, of negligible cross-section, and placed
  one metre apart in a vacuum, would produce
  between these conductors force of 2 x 10-7 N per
  metre of length.

33
Torque on a Rectangular Current-carrying Coil in
a Uniform Magnetic Field

• Let the normal to the coil plane make an angle ?
  with the magnetic field.
• The torque ? is given by

34
Moving Coil Galvanometer

• A moving coil galvanometer consists of a coil of
  copper wire which is able to rotate in a magnetic
  field.
• The magnetic field is produced in the narrow air
  gap between concave pole pieces of a permanent
  magnet and a fixed soft-iron cylinder.
• The coil is pivoted on jewelled bearings and its
  rotation is resisted by a pair of spiral hair
  springs.

35
Radial Magnetic Field

• In order to have a meter with a linear scale, the
  field lines in the gap should be always parallel
  to the plane of the coil as it rotates.
• This could be achieved if we have a radial
  magnetic field. The soft iron cylinder gives us
  this field shape.

36
The Principle of a Moving Coil Galvanometer

• The torque due to the current in the coil is
  given by

• The resisting couple due to the hair springs is

Where ? is the angle of deflection and k is the
torsion constant.

• The coil rotates until

• Then we have

37
Current Sensitivity

• The current sensitivity of a galvanometer is
  defined as the deflection per unit current.

Unit Rad A-1 or mm A-1

• High current sensitivity can be achieved by
• A coil of large area,
• A coil of large number of turns,
• Large value of B which could be achieved by using
  strong magnet and narrow air gap.
• Hair springs with small torsion constant k.

38
Limitation of High Current Sensitivity

• If the coil is too large, the moment of inertia
  is also large and hence the coil would swing
  about its deflection position before a reading
  can be taken.
• If the coil has a large number of turns, the air
  gap needs to be wide.
• If the hair springs have small torsion constant,
  the restoring torque would become weak and the
  coil would swing before coming to rest.

39
Voltage Sensitivity

• The voltage sensitivity of a galvanometer is
  defined as the deflection per unit voltage across
  the galvanometer.

Unit rad V-1 or mm V-1
Where R is the resistance of the galvanometer.

• High voltage sensitivity is desirable in circuits
  of relatively low resistance.