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Magnetic Fields
Objective: I can describe
the structure of
magnetic fields and
draw magnetic field
lines.
magnetism
The earliest magnets were
found naturally in the mineral
magnetite
Magnets produce magnetic
forces and have magnetic
field lines
Magnets have two ends or poles, called north
and south.
Magnetic Fields are strongest near
the poles of the magnet and the
magnetic field lines are closer
together.
Unlike poles of
magnets attract
each other and like
poles of magnets
repel.
The earth is like a giant magnet!
The nickel iron core of the earth gives the earth a
magnetic field much like a bar magnet.
Magnetic Field and Moving Charges
All moving charges create magnetic fields.
Spinning electrons in atomic orbits create magnetic
fields. When the electrons are not spin paired then
the atom is a small magnet.
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magnetic
domains
Magnetic substances
like iron, cobalt, and
nickel are composed
of small areas where
the magnetic fields of
groups of atoms are
aligned. These
regions are called
domains.
When domains of a magnetic substance align
in the same direction a permanent magnet is
formed. These domains are typically
composed of billions of atoms.
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Electricity &Magnetism
Objective: I can use the right
hand rule to determine the
direction of the magnetic filed
near current carrying wire.
I can use right hand rules to
determine forces on moving
charges in magnetic fields.
Objective:
I can use F=BILsinΘ, F =
BqvsinΘ, and B = (μo /2π)
(I/r) to determine the
forces on current carrying
wires and magnetic field
strength near current
carrying wires.
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•
The force on electric current in a magnetic field is
given by
F = BIL sinθ
If the direction of the
current is perpendicular
to the field (θ = 900),
then the force is
Fmax = BIL
The magnitude of B
is defined as
B = Fmax
IL
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The SI Unit for magnetic field B is
the tesla (T). It is clear that 1 T =
1N/Am
Charges in a Magnetic Field
•Moving charges experience
a force due to a magnetic
field.
•FB = B × qv
•Magnitude of FB is:
•FB = Bqv sin Θ
•where is the angle between
v and B.
•Direction is from the right
hand rule.
Magnetic Force on Moving
Charge: Right Hand Rule
• Magnetic Force vector F on
charge q moving with velocity v
• |F| = q|v| |B| sin
• Point the thumb of your right
hand along the velocity vector
v.
• Your fingers point in the
direction of the magnetic field
lines.
• The force on the charged
particle is out of your palm. All
three vectors F, v, B are
perpendicular to each other.
Charges in a Magnetic Field
•If a charge moves perpendicular to a
uniform magnetic field, it will travel in a
circular path. FB or magnetic = Fcentripetal
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Application
•Earth’s magnetic field shields us from
incoming charged particles. However, since
Earth’s magnetic field goes from the south
pole to the north, particles can travel parallel
to the field and enter the atmosphere near
the poles. The “aurora” is the result.
Aurora
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Aurora
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Electricity and Magnetism
All flowing charges including current
create magnetic fields.
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Calculation of Magnetic Field
Near a Long Straight Wire
• Magnetic Field Lines
form loops around the
current, Direction given
by right hand rule.
• The magnetic field
strength B is
proportional to the
current, I, and inversely
proportionate to the
distance from the wire,
r.
Force Between Two Current
Carrying Wires
•F = BIL
•B = F
•
IL
I1
I2
Electromagnet
When an electric current is passed through a
coil of wire wrapped around a metal core, a very
strong magnetic field is produced. This is called
an electromagnet.
Amperes Law,
Magnetic Field inside a long solenoid
• Inside a solenoid of
length L with total of N
windings.
• B =  0 (N/L) I
• B = 0 n l
• n = N/L = windings per
unit length
• Outside the solenoid, the
magnetic field is much
much weaker (but not
exactly zero).
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Sign of Magnetic Flux
• We are free to choose either
direction around a loop to label
as the positive current.
• However, for Lenz law to make
sense, we force our sign
convention for magnetic flux such
that positive current creates
positive self flux (negative current
produces negative self flux).
• A loop with current produces a
magnetic field pattern similar to a
permanent magnetic dipole.
Magnetic Flux
• The Magnetic flux through a
loop is defined as the product
of the area of the surface
bounded by the loop times the
component of magnetic field
perpendicular to the surface.
•  M = A B = A B cos
• B = B cos 
–  measured relative to
perpendicular to surface A
• If the loop has N windings, the
total flux is N  M = N A B cos
B
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External and Self Flux
• Magnetic Flux can come
from an external B-field, or
from the B-field generated by
the current in the coil.
• Solenoid of length L with a
total of N carrying current I
(only case we know how to
calculate exactly)
•Total flux = N M = N A B
•N M = N (r2)  0 (N/L) I =  0 N2 I (r2 /L)
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Electromagnetic Induction
•Mechanical Universe: Electromagnetic
Induction Video
Induction
• Electric field or EMF creates current in a circuit.
• Electric current creates magnetic field
• A CHANGING magnetic FLUX in a circuit induces
an EMF in the circuit. The induced current
produces a magnetic flux that opposes the
change (Lenz’ law).
• EMF =  ( M/t)
• T · m2/s= (Tesla·Coulomb m/s) (m/Coulomb) =
Newton (m/Coulomb) = Joule/Coulomb=Volt
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AC Circuits
and Inductors
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I(t) = I0 sin( t)
Frequency f =  /2
Period = 1/f = 2/
I/t =  I0 cos( t),
AC Voltage required to drive current in
inductor (overcome self EMF)
V = - EMF = L I/t =  L I0 cos( t),
VAC = IAC XL
AC EMF leads current by ¼ oscillation
XL =  L
AC Circuits and capacitors
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I(t) = I0 sin( t)
Q(t) = (I0/ ) sin( t)
VAC = IAC XC
AC Voltage lags current by
¼ oscillation
• XC = 1/( C)
What is a galvanometer?
A galvanometer is an electromagnet that interacts with a
permanent magnet. The stronger the electric current
passing through the electromagnet, the more is interacts
with the permanent magnet.
Galvanometers are
used as gauges in cars
and many other
applications.
The greater the current passing through the wires, the stronger the
galvanometer interacts with the permanent magnet.
What are electric motors?
An electric motor is a device which changes electrical
energy into mechanical energy.
How does an electric motor work?
Go to the next slide 
Simple as that!!
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We have seen how electricity can produce a magnetic
field, but a magnetic field can also produce electricity!
How?
What is electromagnetic induction?
Moving a loop of wire through a magnetic field produces
an electric current. This is electromagnetic induction.
A generator is used to convert mechanical energy into
electrical energy by electromagnetic induction.
Carefully study the next diagrams:
Direct current versus alternating current –
AC vs DC : What’s the difference?
Direct current is electrical current which comes from a
battery which supplies a constant flow of electricity in one
direction.
Alternating current is electrical current which comes from
a generator. As the electromagnet is rotated in the
permanent magnet the direction of the current alternates
once for every revolution.
Go to this website and click the button for DC then for AC
to visually see the difference between the two.
You can see that the DC source is a battery – current
flows in one direction. The AC source is the generator
and the current alternates once for each revolution.
Flux in Transformer
 = flux through a single winding or either coil. (produced by
currents in either or both circuits)
EMF(primary) =  NP /t
EMF(secondary) =  NS /t
P / S = NP / NS
Energy conservation requires
P IP = S IS
P / S = NS / NP