Download Sources of Magnetic Field

Magnetic Field
• A magnetic field is a region in which a
body with magnetic properties experiences
a force.
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.
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.
Magnetic Flux Pattern
The Earth’s 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.
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.)
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
I
Fleming’s 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!
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.



F  I  B
F  I sin 
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.
F
B
I
Unit : tesla (T)
or gauss (G), 1 G = 10-4 T
or weber/m2
Typical Values of the magnetic
flux density
Source
B-Field (Tesla)
Human Brain
10-12
Interstellar Space
10-10
Near Household Wiring
10-4
Sunlight
3x10-5
Earth's Magnetic Field at Pole
5x10-4
Sunspots
.3
Largest man-made Magnet
5.0
Surface of a Nucleus
106
Magnetic Field Measurements
• Using a current balance (d.c.)
• Using a search coil (a.c.)
• Using a Hall probe (d.c.)
Magnetic flux density due to a
straight wire
• Experiments show that the magnetic flux
density at a point near a long straight wire is
I
B
r
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.
Calculation of B near a wire
o I
B
2r
Where o is called the permeability of free space.
 o  4 107 T m A -1 (H m -1 )
Permeability is a measure of the effect of a material
on the magnetic field by the material.
Magnetic Field due to a Solenoid
• The magnetic field is strongest at the
centre of the solenoid and becomes
weaker outside.
Magnetic Flux Density due to a
Solenoid
• Experiments show that the magnetic flux
density inside a solenoid is
N
B  I and B 

So we have
 o NI
B

or B   o nI
N
where n 

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.
1
• At a point at the end of the solenoid, B'   o n
2
B
B   o nI
B' 
 12 
0
1
2

1
 o n
2
Distance from the
centre of the
solenoid
Magnetic Flux Density due to Some
Current-carrying conductors(1)
• Circular coil B 
• Helmholtz coils
 o NI
2r
8 o NI
 o NI
B
 0.72
r
125r
Magnetic Flux density due to Some
Current-carrying Conductors (2)
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.
F  qvB sin 
Fmax  qvB for v  B
F  0 for v // B
http://webphysics.davidson.edu/physlet_resources/bu_semester2/c12_force.html
Right Hand Rule
• Direction of force on a positive charge given
by the right hand rule.



F  q v B
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.
Mass Spectrometer
• The mass spectrometer is used
to measure the masses of atoms.
• Ions will follow a straight
line path in this region.
qE  qvB
• Ions follow a circular
path in this region.
mv2
qvB'
r
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.
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/auroras/selfguide1.html
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.
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.
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.
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.
Force between two parallel
current-carrying straight wires (1)
1. Parallel wires with current flowing in the
same direction, attract each other.
2. Parallel wires with current flowing in the
opposite direction, repel each other.
Force between two parallel
current-carrying straight wires (2)
 o I1 I 2 
F
2a
• Note that the force exerted on I2 by I1 is equal
but opposite to the force exerted on I1 by I2.
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.
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   NBAI sin 
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.
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.
The Principle of a Moving Coil
Galvanometer
• The torque due to the current in the coil is
given by   NBAI
• The resisting couple due to the hair springs
is  '  k
Where  is the angle of deflection
and k is the torsion constant.
• The coil rotates until
  '
NBAI
• Then we have  
k
i.e.  I
Current Sensitivity
• The current sensitivity of a galvanometer is
defined as the deflection per unit current.

NBA

I
k
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.
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.
Voltage Sensitivity
• The voltage sensitivity of a galvanometer is
defined as the deflection per unit voltage
across the galvanometer.
 NBA
Unit : rad V-1 or mm V-1
V

kR
Where R is the resistance of the galvanometer.
• High voltage sensitivity is desirable in
circuits of relatively low resistance.