Download Sources of Magnetic Field

MAGNETIC FIELD
 ENROLLMENT NO.
 NAME.
130280111105
KARAN SHARMA
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
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B 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
0.3
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
•This 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
B  I and
So we have
 o NI
B

or B   o nI
N
where n 

N
B

Variation of magnetic flux density along the
axis of a solenoid
 B is independent of the shape or area of the crosssection of the solenoid.
 At a point at the end of the solenoid,
1
B' 
B
2
 o n
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 Currentcarrying conductors(1)
• Circular coil B 
 o NI
2r
Where r is the radius of the coil
• Helmholtz coils
8 o NI
 o NI
B
 0.72
r
125r
Where r is the separation of
the coil
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
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.
Hall Effect
http://maxwell.ucdavis.edu/~electro/magnet_force/hall.html
 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 currentcarrying straight wires (1)
1.
2.
Parallel wires with current flowing in the same
direction, attract each other.
Parallel wires with current flowing in the
opposite direction, repel each other.
Force between two parallel currentcarrying 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 Current Loop
 A loop of wire carrying a current experiences a
torque.
 This torque can cause it to rotate up to 1800
  = NBAI
Moving Coil Galvanometer
 A galvanometer that is operated by the force exerted by
an electric current flowing in a movable coil suspended
in a magnetic field.
Construction of a Moving Coil Galvanometer
Linear scale
pointer
Concave pole piece
Moving coil
Soft iron cylinder
Hair spring
Moving Coil (1)
 A coil, with current I flowing through it,
placed in a magnetic field, can experience a
torque .
  = NBAI
Moving Coil (2)
 The moving coil is hung from a
spring which winds up as the coil
rotates; this winding up produces
a restoring torque ’ proportional
to the winding up (or twisting) of
the spring, i.e. to the angular
deflection of the coil .
 ’ = c
 The coil comes to equilibrium
when  = ’
Radial Field
 In order to have a meter with a linear scale,
the angle between the coil and the field must
remain constant.
 The angle can remain constant (90°) if we
have a radial magnetic field.
 The soft iron cylinder gives us this field shape.
Current Sensitivity (1)
 The current sensitivity is defined as the deflection per unit
current.


I
NBA

c
Unit : rad/A
or mm/A
Current Sensitivity (2)
The current sensitivity can be increased by
 Increasing the number of turn of coils
but the armature will be too bulky and the size of
the air gap cannot be too small.
 Increasing the magnetic field in the air gap
stronger magnet is used and the air gap should be
as narrow as possible.
 Increasing the area of the coil
but the coils will swing about its deflected position.
 Using weaker hairspring,
but if the opposition of the suspension is too weak
the coil will also swing about its deflected position.
(reading again take time).
Voltage sensitivity
 The voltage sensitivity is defined as the deflection
per unit voltage.

NBA
 
V
cR
Unit : mm/A
d.c. Motor
http://www.physclips.unsw.edu.au/jw/electricmotors.html
Velocity selector for charged particles
 The speed can be obtained from the equation
 q v B = q E, or v= E / B