Download Magnetism - Eastside Physics

Magnetism
• Magnets are used in meter, motors,
speakers, CDs, MRIs, cyclotrons and to
store computer data.
• They are used to move heavy objects,
propel trains and store antimatter.
• Changing magnetic fields will produce
electricity
Magnets
• A magnet consists of of a north and south
pole which attract each other. No matter
how many time a magnet is cut all pieces
will have a N and S pole. Unlike an electric
charge, magnetic poles do not exist by
themselves.
• Soft metal (iron) is easily magnetized and
easily loose that magnetism.
Cont.
• Hard metals, (cobalt, nickel) are difficult to
magnetize, but retain their magnetism
• Permanent magnets can be created by close
proximity to magnetic material.
• Electromagnets occur due to the presents of
an electric current that temporarily polarizes
a metal core.
• Magnetic field surround magnetized material
moving from north to south pole. (a vector)
Earth’s Magnetic Field
• A small magnetic bar (compass) will seek
out earth’s magnetic field. S end of the bar
points north and the N end points south.
• The magnetic axis of earth is 11o tilt to the
axis of rotation. (magnetic declination)
• At the equator a compass needle will be
horizontal. Further N or S the needle will
additionally tilt towards the earth.(dip angle
Cont.
• Earth’s magnet field is coursed by an electric
current in the rotating liquid part of the
earth’s core and earth’s rotation. Jupiter that
rotates faster has a stronger magnetic field.
• Every few million years the earth’s magnetic
field reverses. (evident in basalt rock)
• Some birds use earth’s magnetic field to
migrate and anaerobic bacteria have
magnetite as part of their internal structure.
Magnetic Fields
• When a charged particle moves through a
magnetic field the field’s force acts on the
particle. It is maximum when the movement
is perpendicular to the field and zero when
moving parallel to the field.
• Magnetic force ( B ) on a moving charge is
directed perpendicular to the magnetic field.
Fields cont.
• The magnetic force on a charged particle is
proportional to the charge q, (C) the velocity
of the charge v,(m/s) the magnitude of the
field B (tesla T = weber Wb/m2 ) and the
angle of movement to the field.
• F = qvBsin at 90o Fmax = qvB
• 1 C moving at 1 m/s in a field of 1 T
experiences a force of 1 N
• In cgs units 1 T = 104 G (gauss)
Electric Force on a
Current-Carrying Conductor
• Like a single charge , magnetic force is
exerted on a current carrying wire. The
force on the wire is the sum of the
individual forces on the charged particles.
• Consider a length of wire = l, with crosssectional area A, carrying a current I in a
magnetic field B. The velocity = vd and n is
the number of unit carriers per unit volume.
Cont.
• Then Fmax = (Qvd B)(nAl)
• as I = nqvdA then Fmax = BIl *
• *this equation is only true when current and
magnetic field are at right angles to each other.
• If the wire is at some angle to the field then
F = BIlsin where  is the angle between the
field and current. If the current is in the , or
opposite the direction of the field the force is
zero.
Torque on a Current Loop and
Electric Motors
• If a loop of wire is placed in a magnetic field
a torque is exerted on a flowing current in b.
I
B
b
a
Force on a
is zero,
Force on b
F1=F2=BIb
Cont.
• The direction of the force on the left side is
out and the direction on the right side is
in.(right hand rule)
• Viewed from the side
a/2
F1
Rotate around
O clockwise
O
F2
B
Cont.
• Torque = force x distance
• T = F1(a/2) + F2(a/2)
= BIb(a/2) +BIb(a/2)
= BIab
As the area of the loop = A = ab then
Tmax = BIA only if field is parallel to loop
• If the field makes an angle with the loop
T = BIAsin
Torque on a Coil
•
•
•
•
•
Let N = the number of turns in a coil
then T = BIAN sin
Let  = IAN ( magnetic moment of coil)
then T = B sin
where  is the angle between the magnetic
moment and the magnetic field.
Electric Motors
• Motors convert electric energy to kinetic
energy of rotation by use of a current
carrying coil loop rotating in a magnetic
field. Because the angle between loop and
field as the loop rotates goes from 90 to 0,
when it passes 0 it will reverse unless the
current reverses direction. In an AC current
this occurs 120 times per second allowing
continual rotation.
DC motors
• In a DC motors current reversal is
accomplished mechanically with a split ring
contact ( commutators) and brushes. As the
brushes cross the gaps in the ring they cause
the loop current to change direction. This
change in direction of current causes
continual rotation.
Right Hand Rule
• To determine the direction of magnetic force
with respect to motion and magnetic field, use
the right hand rule.
• 1) point fingers of right hand in the direction
of the velocity
• 2) curl the fingers in the direction of the
magnetic field, moving through the smallest
angle
• 3)The thumb points in the direction of the
magnetic force exerted on a positive charge
Charged Particle Motion in a
Magnetic Field
• When the velocity of a charged particle is
perpendicular to a uniform magnetic field, it
moves in a circular path perpendicular to
that field. The magnetic force is always
directed to the center of the circular path,
thus causing centripetal acceleration.
• F = qvB = (mv2)/r or r = (mv)/(qB)
• The latter is called the cyclotron equation
Cont.
• The radius of the path is proportional to the
momentum and inversely proportional to
the charge
• If the initial direction of the velocity is not
perpendicular to the magnetic field the path
followed by the particle is a helix (spiral),
along the magnetic field lines.
Magnetic Field Caused by a
Conductor
• If a constant current is passed through a long
conductor a circular magnetic field forms
around the conductor. Using the RHR, point
thumb in the direction of the positive current
and curled fingers point in the direction of the
magnetic field.
• The strength of that field is given by
B = ( oI)/(2r) where o = 4 x 10-7 T.m/A
Ampere’s Law
• Consider an irregular shaped path around a
magnetic field. The length of the path can be
divided into small segments of l. Multiplying
this segment by the magnetic filed parallel to
it gives BIIl. Ampere’s Law states that the
sum of all the products over a closed path is
equal to 0 x I (Current passing through the
closed path)
• Ampere’s circuital law  BIIl = 0 x I
Magnetic Force Between Two
Parallel Conductors
• Two long parallel wires separated by
distance d carrying currents I1 and I2 will
exert a magnetic force upon each other due
to the magnetic fields they each create.
• The magnetic field created by wire 2 is
given by B2 = (oI2)/(2d) The force on
wire 1 due to B2 is
F1 = B2I1l = [(oI2)/(2d)]I1l= (oI2 I1l)/(2d)
Cont.
• Parallel conductors carrying currents in the
same direction attract each other
• Parallel conductors carrying currents in
opposite directions repel each other.
Magnetic Fields of Current
Loops and Solenoids
• If a current carrying conductor is formed
into a loop the magnetic field is enhanced
by the fact that opposite positions on the
loop reinforce each other ( have the same
magnitude). The magnetic field produced is
at the center of the loop.
• The magnitude is given by B = (oI)/2R
• where R is the radius of the loop.
Cont.
• When a coil has N loops each carrying
current I, the magnetic field at the center is
given by B = N[(oI)/2R]
• The formation of this coiled wire carrying a
current is called a solenoid, (electromagnet).
• Only when current flows is it a magnet and
its strength increases with an increase in
current strength and number of coils per unit
length.
Cont.
• The magnet field lines inside a solenoid are
nearly parallel and produce a field stronger
that outside the solenoid. The field inside
the solenoid has a constant magnitude.
Outside the solenoid the field lines move in
the opposite direction, are not uniform and
form a weaker field. North = direction of I
• Field magnitude inside B = onI n = N/l
Magnetic Domains
• Considering that an electron ( a charged
particle ) moves in a circular orbit, it
produces a magnetic field of the order of
20T, at the center of the orbit. Atoms should
be large scale magnets except that the effect
of one electron cancels out the effect of its
partner. Most electrons are paired and of
opposite spin causing most material not to
be magnetic.
Cont.
• In certain materials, cobalt, iron and nickel not
all electrons are paired completely and thus not
all magnetic fields cancel. These are called
ferromagnetic materials. In such materials
coupling occurs between neighboring atoms,
forming large groups of atoms with spins that
are aligned. (domains)
• When domains are randomly arranged the
material is not magnetized. An external field
can align domains resulting in magnetization.