Download The Magnetic Field

The Magnetic Field
Physics
Montwood High School
R. Casao
• Our most familiar experience of magnetism is through
permanent magnets.
– Inside a magnetized body, such as a permanent magnet, there is
a coordinated motion of certain electrons; in an unmagnetized
body, the electron motions are not coordinated.
• These are made of materials which exhibit a property we
call “ferromagnetism” - i.e., they can be magnetized.
• An unmagnetized piece of iron can become a permanent
magnet by being stroked with a permanent magnet
• If a piece of unmagnetized iron is placed near a strong
permanent magnet, the piece of iron will eventually
become magnetized.
• A magnetized object can lose its magnetic properties by
heating and cooling the iron or by hammering the iron.
• Magnetic materials can be described as hard or soft,
depending upon the extent to which they retain their
magnetism.
– Soft magnetic materials, such as iron, are easily magnetized but
also tend to lose their magnetism easily.
– Hard magnetic materials, like cobalt and nickel, are difficult to
magnetize, but once they are magnetized, they tend to retain
their magnetism.
• The magnetic properties of many materials are explained
in terms of a model in which an electron is said to spin on
its axis (remember the up and down arrows in the orbital
notation you used in chemistry ).
– The spinning electron is a charge in motion that produces a
magnetic field.
• In atoms with many electrons, the electrons usually pair up
with their spins opposite each other, and their magnetic fields
cancel each other. This is why most substances are not
magnetic.
• In ferromagnetic materials such as iron, cobalt, and nickel, the
magnetic fields produced by the electron spins do not cancel
completely.
• Strong coupling occurs between neighboring atoms to form
large groups of atoms whose net spins are aligned; these
groups are called domains.
• In an unmagnetized substance, the magnetic domains are
randomly oriented.
• In magnetized materials, whether
permanent or temporary, the domains
are aligned.
•
unmagnetized
magnetized
– In hard magnetic materials, the domain alignment remains after
the external magnetic field is removed.
– In soft magnetic materials, once the magnetic field is removed,
the random motion of the particles in the material changes the
orientation of the domains back to a random arrangement.
– Heating and hammering can cause the domains in hard
magnetic materials to become randomly arranged, resulting in a
loss of the permanent magnetic properties.
• Depending on how we position two magnets, they will
attract or repel, i.e. they exert forces on each other.
• Thus, a magnet must have an associated field:
a magnetic field.
• We describe magnets as having two magnetic poles:
North (N) and South (S).
• Magnetic poles always occur in pairs.
• When a magnet is broken in half, equal and opposite
poles appear at either side of the break point.
• The result is two magnets, each with a north and south
pole.
• A compass is used to detect the presence of a magnetic
field.
– The needle of a compass is a piece of magnetized iron.
– The compass needle aligns with the magnetic field at the
needle’s position.
– The north pole of a compass needle is attracted toward the
geographic north pole of the Earth and repelled by the Earth’s
geographic south pole.
• An object that contains iron but is not itself magnetized
(shows no tendency to point north or south) is attracted
by either pole of a permanent magnet.
– This is the attraction that acts between a magnet and the
unmagnetized steel door of a refrigerator.
• Only iron and a few other materials, such as cobalt,
nickel, gadolinium, and some of their oxides and alloys,
show strong magnetic effects and are said to be
ferromagnetic.
• Other materials show more slight magnetic effect.
• The Earth itself is a large magnet.
– Geophysicists generally agree
that the Earth’s magnetic poles
arise from currents in its molten
iron core.
– The magnetic poles are offset
slightly from the geographic
poles of the Earth’s rotation axis.
– The geographic north pole is actually a
south magnetic pole.
• We used the concept of an electric field surrounding an
electric charge.
• Similarly, we can imagine a magnetic field surrounding a
magnet.
– The force one magnet exerts on another can be described as the
interaction between one magnet and the magnetic field of the
other.
– We can also draw magnetic field lines.
• For magnetic field lines:
– The number of lines per unit area is proportional to the strength
of the magnetic field. The field lines are closer together where
the magnetic field is stronger.
– The direction of the magnetic field is tangent to a field line at
any point.
• The direction of the magnetic field at a given point is
defined as the direction that the north pole of a compass
needle would point if placed at that point.
• Magnetic field lines always point out from the north pole
and toward the south pole of a magnet.
• Magnetic field lines continue inside the magnet to form
closed loops.
• The origin of magnetism lies in moving electric charges.
Moving (or rotating) charges generate magnetic fields in
the surrounding space in addition to its electric field.
• An electric current generates a magnetic field.
• A magnetic field will exert a force on a moving charge
that is present in the field.
• A magnetic field will exert a force on a
conductor that carries an electric current
in the field.
• The magnetic field is a vector field
associated with each point in space.
– The symbol for the magnetic field if B.
• We can define a magnetic field B at a point in space in
terms of the magnetic force FB that the field exerts on a
charged particle moving with a velocity v.
• Experiments on charged particles moving in a magnetic
field give the following results:
– The magnitude FB of the magnetic force exerted on the particle
is proportional to the magnitude of the charge q.
• If a 1 μC charge and a 2 μC charge move through the same
magnetic field with the same velocity, experiments show
that the force on the 2 μC charge is twice as great as the
force on the 1 μC charge.
– The magnitude FB of the magnetic force exerted on the particle
is proportional to the magnitude, or strength, of the field B.
• If we double the magnitude of the field without changing
the charge or its velocity, the force doubles.
– The magnitude FB of the magnetic force exerted on
the particle is proportional to the speed v of the
particle.
• A charged particle at rest experiences no magnetic force.
– The magnetic force FB does not have the same
direction as the magnetic field B but instead is always
perpendicular to both B and the velocity v.
• The magnitude FB of the magnetic force is proportional to
the component of the velocity perpendicular to the field.
The maximum magnetic force FB occurs when the magnetic
field B and the velocity v are at right angles to each other.
• The magnetic force FB is zero when the magnetic field B
and the velocity v are parallel (0º) or antiparallel (180º).
• The direction of FB is always perpendicular to the plane
containing B and v.
• Equation: F  q  v  B  q  v  B  sin 

– q is the magnitude of the charge (drop any negative signs on
charges)
–  is the angle between the direction of v and the direction of B.
• The direction of the magnetic force FB is
given by the right hand rule:
– Point the fingers of your right hand in the
direction of the velocity vector v.
– Point the palm of your right hand in the direction
of the magnetic field vector B.
– The thumb of your right hand points in the
direction of the magnetic force FB.
Casao’s Version of the Right-Hand Rule
• I use the right hand as described for positive charges.
No change here.
• I use the left hand for negative
charges.
– Point the fingers of the left hand
in the direction of the velocity
vector v.
– Point the palm of the left hand
in the direction of the magnetic
field vector B.
– The thumb of the left hand points
in the direction of the magnetic
force FB.
• If the magnetic field B is directed into the page, crosses
represent the tail of the vector arrow.
• If the magnetic field B is directed out of the page, dots
represent the head of the vector arrow.
• The units of the magnetic field B is the Tesla and the
abbreviation is T.
1T  1
N
C m
1
s
N s
N
1
C m
A m
• An older unit for the magnetic field is the Gauss (1 G =
0.0001 T).
Magnetic Force on a Current-Carrying
Conductor
• A magnetic force is exerted on a single charged particle
when the particle moves through a magnetic field, so a
current-carrying wire placed in a magnetic field also
experiences a magnetic force.
• Current is a collection of many charged particles in
motion, so the resultant force exerted by the magnetic
field in the wire is the sum of the individual forces
exerted on all the charged particles making up the
current.
• The force exerted on the particles is transmitted to the
wire when the particles collide with the atoms making up
the wire.
• The force on a current-carrying conductor can be
demonstrated by hanging a wire between the poles of a
magnet.
• Equation:
F  I  l  B  I  l  B  sin 
– l is the length of the wire in the
magnetic field.
–  is the angle between the length of
the wire (or the direction of the
current) and the magnetic field.
• The direction of the magnetic
force is found using the right
hand rule.
– Fingers in the direction of I.
– Palm in direction of B.
– Thumb points in direction of FB.
• A current consists of charge carriers q moving with
velocity v.
Magnetic field around a long, straight current-carrying wire
Forces Between Two Current-Carrying
Wires
• Currents traveling in
the same direction
result in an attractive
force acting between
the two wires.
• Currents traveling in
opposite directions
through two wires
produce a repulsive
force between the two
wires.
• Force between two parallel
wires:
o  l  I1  I 2
F 
2 d
μo =4·π x 10-7 T·m/A
l = length of conducting wire
d = distance between wires
Notice that opposites (· and x)
attract and unlike (· and ·
or x and x) repel.
Motion of a Charged Particle in a
Uniform Magnetic Field
• When a charged particle traveling with velocity v enters
a uniform magnetic field perpendicular to the magnetic
field, the particle moves in a circle in a plane
perpendicular to the magnetic field.
• The particle moves in a circle
because the magnetic force FB is
at right angles to v and B and has
a constant magnitude q·v·B.
• As the force deflects the particle,
the directions of v and FB change
continuously.
• Because FB always points toward the center of the circle,
it changes only the direction of the velocity and does not
affect the magnitude of the velocity.
• Motion of a charged particle under the action of a
magnetic field alone is always motion with constant
speed.
• The right hand rule can be used to
determine the direction of the force
acting on the charged particle.
• Because the particle moves under
the influence of a constant force
that is always at right angles to the
velocity of the particle, the path
is a circle of constant speed v.
• The inward directed magnetic force FB provides the
centripetal force FC to keep the particle traveling in a
circular path.
FB  FC
m v
q  v  B ·B
r
m v
q B 
r
2
Mass Spectrometry
• An analytical technique for measuring the mass-to-charge ratio
(m/q) of ions in the gas phase.
– Mass spectrometry is our most valuable analytical tool fr
determining accurate molecular masses.
– Can also give information about structure.
– Proteins can now be sequenced by mass spectrometrya.
• A mass spectrometer is designed to do three things:
– Convert neutral atoms or molecules into a beam of positive
(or rarely negative) ions.
– Separate the ions on the basis of their mass-to-charge (m/q)
ratio.
– Measure the relative abundance of each ion.
• Schematic for an electron ionization mass
spectrometer (EI-MS).
• Accelerating is done by an electric field; bending is
done by a magnetic field.
• Work done on charge by electric field
increases the kinetic energy of the charge:
q·V = ½·m·v2
m v
q B 
r
• Distance of separation from point of entry to
collection point: d = 2·r
Magnetic Field of a CurrentCarrying Wire
• A current-carrying wire produces a
magnetic field and can be detected by a
compass needle placed near the wire.
• When no current is in the wire, all needles
point in the direction of the Earth’s
magnetic field.
• When the wire carries a strong, steady
current, the needles deflect in directions
tangent to the circle around the wire,
pointing in the direction of the magnetic
field B due to the wire.
• A current-carrying wire produces a
magnetic field and can be detected by a
compass needle placed near the wire.
• When no current is in the wire, all needles
point in the direction of the Earth’s
magnetic field.
• When the wire carries a strong, steady
current, the needles deflect in directions
tangent to the circle around the wire,
pointing in the direction of the magnetic
field B due to the wire.
• If the current is reversed, the needles
reverse directions.
• Right hand rule for
determining the direction of
the magnetic field around a
current carrying wire: if the
wire is grasped in the right
hand with the thumb in the
direction of the current I, the
fingers will curl around the
wire in the direction of the
magnetic field B.
• The magnetic field lines form
concentric circles around the
wire.
• The magnitude of B is the same everywhere on a
circular path centered on the wire and lying in a plane
perpendicular to the wire.
• The magnetic field strength increases as the current I increases.
• The magnetic field strength decreases as the distance from the
wire increases.
o  I where r is the distance from the
• Equation: B 
2    r wire to the location of the
μo =4·π x 10-7 T·m/A
magnetic field
Current Loops and Solenoids
• The right hand rule can also be applied to find the direction of the
magnetic field of a current-carrying loop.
• No matter where on the loop you apply the right hand rule, the
field within the loop points in the same direction.
• If a long, straight wire is bent into a coil of several
closely spaced loops, the resulting device is called a
solenoid.
• Solenoids produce a strong magnetic field by combining
several loops.
• The solenoid has many applications because it acts as a
magnet when it carries a current.
• The magnetic field inside a solenoid increases with the
current and the number of coils per unit length.
• The magnetic field of a solenoid can be increased by
inserting an iron rod through the center of the coil; this
device is often called an electromagnet.
– The magnetic field that is induced in the iron rod adds to the
magnetic field of the solenoid, creating a more powerful
magnet.
• In a car or truck, the starter solenoid helps to start the
vehicle. The starter solenoid receives a large electric
current from the battery and a small electric current
from the ignition switch.
• When the ignition switch is turned on (when the key is
turned to start the car), the small electric current forces
the starter solenoid to close a pair of heavy contacts, thus
relaying the large electric current to the starter motor.
• If a starter solenoid receives insufficient power from the
battery, it will fail to start the motor, and may produce a
rapid 'clicking' or 'clacking' sound.
• This can be caused by a low or dead battery, by corroded
or loose connections in the cable, or by a broken or
damaged positive (red) cable from the battery.
• Any of these will result in some power to the solenoid,
but not enough to hold the heavy contacts closed, so the
starter motor itself never spins, and the engine is not
rotated and does not start.
• Magnetic field inside a solenoid:
μo =4·π x 10-7 T·m/A
• The quantity
unit length l:
N
μo  N  I
B
l
l is the number of turns per
n
N
l
• Magnetic field B inside a solenoid:

B  μo  n  I