Download Magnetism

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Magnetism
A Brief Historical Interlude

Greek scholars and scientists discovered certain types of rocks, called lodestones,
which would attract small pieces of iron; this demonstrated the existence of a
magnetic force. These lodestones were discovered in a province of Greece known
as Magnesia. It is from the name of this region that we get the term magnet.

At first, magnets served as an interesting conversation piece and a cool “magic”
trick. However, people soon started to see some practical uses for these strange
pieces of rock. It was discovered by the Chinese that small fragments of these
lodestones would tend to rotate and orient themselves in a particular direction:
North(ish). By harnessing these tiny fragments, Chinese sailors invented the first
navigational compasses in the 12th century.

The question, though, was why? Why do these small pieces of rock (and
eventually metal) turn and point to the North? It was suggested in the 16th century
by the British physician William Gilbert that a compass will always point North
because the Earth itself has some inherent magnetic properties. {This should
make sense; lodestones are rocks found in the Earth. Isn’t it likely that, if pieces
of the Earth could be magnetic, then the Earth itself could be magnetic as well?}
Electromagnetism

During the early stages of experimentation with magnetism, it was seen as a
wholly new phenomenon that was unrelated to other discoveries. In fact,
experiments were being conducted in magnetism and electricity concurrently, and
the two fields developed independently until 1820, when…

One of the great discoveries in the field of magnetism was made by the Danish
professor Hans Christian Oersted as he was preparing a lecture for his students.
He was attempting to show that electricity and magnetism were unrelated by
showing that a compass would be unaffected by an electric current. However,
much to his surprise, when a current was directed near a compass, the compass
needle was seen to move! Oersted had discovered, completely contrary to his
initial intentions and to his total surprise, that an electric current could indeed
affect a compass.

Evidence began to show up from other scientists confirming Oersted’s discovery.
Eventually, the French physicist Andre-Marie Ampere (after whom the unit for
electric current is named) proposed that all magnetic phenomena is the result of
electric currents.*
{*It is imperative to recall at this time that an electric current is simply the flow
of charged particles from one location to another}
Magnetism Notes
Physics
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Bradshaw 04-05
Ed. 2010
Name _________________________________________________
Period _______
Forces and Fields

When talking about Electrostatics, we said that there exists a force between any
two charged objects. Furthermore, we defined this force as the interaction of two
electric fields. (Recall that an Electric Field is created due to the presence of a net charge.)
The Magnetic Force (FB) is a result of the interaction
of two magnetic fields (B).

In electrostatics, we used a very simple rule for determining the direction of the
Electrostatic Force: Opposites Attract (Paula Abdul, anyone?). With magnetism,
there is a similar rule, although there is a key difference. In magnetism, we refer
to the “magnetic poles” as being North and South; much like electric charges, the
opposite poles of a magnet will attract, while the like poles will repel. {Note: the
use of the term ‘pole’ is almost certainly a result of the geographic term.}

In electrostatics, it is perfectly acceptable and very common to find a solitary
positive charge or negative charge. In magnetism, it is IMPOSSIBLE to locate a
solitary North or South pole. In other words, there is no such thing as a magnetic
monopole. So every magnet, regardless of its size or strength, must have a North
and a South pole; in fact, many magnets have multiple North and South poles.
{Recent studies and research have hinted at the possible existence of magnetic
monopoles; however, none have currently been isolated or identified.}

In electrostatics, the direction of the electric field is defined such that it points
away from a positive charge and towards a negative charge. Similarly, the
direction of Magnetic Field lines always point in such a manner that they go
away from the North Pole and towards the South Pole.

Magnetic fields are produced by moving charges. This could be either a single
charge q moving with a speed v, or an electric current. When either of these two
scenarios takes place, a magnetic force can be observed.
o The S.I. unit for measuring the strength of the magnetic field is called the
Tesla (T). It is named after one of the most interesting personalities in all of
Physics, Nikola Tesla
o The Earth’s magnetic field strength is approximately BEarth
Magnetism Notes
Physics
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= 5 E-5 T .
Bradshaw 04-05
Ed. 2010
Name _________________________________________________

Period _______
A Moving Charge in a Magnetic Field
q moves with a speed v through a magnetic field B, it will
experience a magnetic force FB. The magnitude of this force is given by
o When a charge
FB = qvBSin
where  is the angle between the direction of v and B. This angle is often
(but not always) 90 degrees. We will find that the maximum amount of force
will be found when the angle = 90 (or 270) degrees; conversely, we find that
there is zero force when the angle is 0 (or 180) degrees.
o The direction of this force is determined in a very peculiar manner known as
the “Right Hand Rule.” Assuming the charge is positive, you point the
fingers of your right hand in the direction of the charge’s velocity (v). While
doing this, you face your palm in the direction of the magnetic field (B) [this
can be envisioned as the direction in which your fingers will bend]. When
you stick out your thumb (your hand should now look like you are trying to
shake hands with someone) it points in the direction of the magnetic force
(FB). To recap:
Fingers
Palm/Bend
Fingers
V
B
Thumb
FB
Velocity
Magnetic
Field
Magnetic
Force
o What this indicates is that the plane the magnetic force resides in is
perpendicular to the plane that the velocity is in, and it is perpendicular to the
plane that the magnetic field is in. In other words, we are dealing with a
three-dimensional situation here folks.
 {Note: If the moving charge happens to be a negative charge, we use
the same rule but use our left hands.}
Magnetism Notes
Physics
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Bradshaw 04-05
Ed. 2010
Name _________________________________________________

Period _______
An Electric Current in a Magnetic Field
o When a current-carrying wire of length
L
carries a current
magnetic field B, the wire will feel a magnetic force
this force is given by
FB.
I
through a
The magnitude of
FB = ILBSin

where  is the angle between the direction of I and B. This angle is often
(but not always) 90 degrees. We will find that the maximum amount of force
will be found when the angle = 90 (or 270) degrees; conversely, we find that
there is zero force when the angle is 0 (or 180) degrees.
o The direction of this force is determined by the “Right Hand Rule.” You
point the fingers of your right hand in the direction of the current (I). While
doing this, you face your palm in the direction of the magnetic field (B) [this
can be envisioned as the direction in which your fingers will bend]. When
you stick out your thumb (your hand should now look like you are trying to
shake hands with someone) it points in the direction of the magnetic force
(FB). To recap:
Fingers
Palm/Bend
Fingers
I
B
Thumb
FB
Current
Magnetic
Field
Magnetic
Force
o In order to express vectors in three dimensions (because we have a threedimensional situation) we need a way to show a vector that indicates
directions of depth (i.e., away and towards). To do this, we naturally turn
to… archery.
o Picture an arrow. It has a pointed end, and it has a fletched (or feathered) end.
If someone shot an arrow at you, as you watched it approach, you would see a
dot coming towards you… and then it would be embedded in your forehead.
However, you would see a dot. If you shot an arrow away from you, you
would see the criss-cross of the fletching, and it would appear like an ‘x’. As
a result, we use the following system to represent these directions:
Magnetism Notes
Physics
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Bradshaw 04-05
Ed. 2010
Name _________________________________________________
Period _______

So now, we must ask ourselves: where do these magnetic fields come from?
Well, it can be shown that, due to a process known as Induction, all magnetic
fields are the result of electric currents.

Magnetic Field produced by an Electric Current
I flows through a wire, the flowing charges will
produce a magnetic field B that circles around the wire (like water circling a
drain) and is weaker the farther R away from the wire you get. This magnetic
o When an electric current
field is given by
B = 0I
2R
0 is a constant known as the
value of 0 = 4 E -7 T*m/A .
where
Permeability of Free Space; it has a
o The S.I. unit of the magnetic field is the Tesla (T).
o To determine the direction of this magnetic field, we have a 2nd “Right Hand
Rule”: point your right thumb along the wire in the direction that the current is
flowing. Then wrap your fingers around the wire as if you were trying to
grasp it; the magnetic field will circle the entire wire in the direction that your
fingers want to curl. {See diagrams below.}
Magnetism Notes
Physics
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Bradshaw 04-05
Ed. 2010
Name _________________________________________________
Period _______
Note: the following two diagrams are describing the exact same magnetic fields
Magnetism Notes
Physics
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Bradshaw 04-05
Ed. 2010
Name _________________________________________________

Period _______
Magnetic Field inside a Solenoid
o A Solenoid is formed when a long straight wire is looped around a
cylindrical center (think of a Slinky™). As current flows through the
wire, a magnetic field is established that circles the wire according to what
we have previously seen. However, due to the loop nature of the solenoid,
what we will find is that, for each successive loop, the magnetic field will
pass directly through the center of the solenoid. This essentially creates a
linear magnetic field.
o Assume that we have a solenoid with a length
L
that is formed by a
number N of individual loops of wire. Assuming that L is much greater
than the radius of the loop of the solenoid, when the solenoid carries a
current I we can determine the strength of the magnetic field inside the
solenoid as
B = 0IN
L
where 0
= 4 E -7 T*m/A .
o The direction of this magnetic field is also found via the Right Hand Rule.

Magnetic Force between two parallel current-carrying wires
o In the diagram above, Wire 1 is parallel to Wire 2. Wire 1 carries a
current I1 and Wire 2 carries a current I2. The wires each have a length L
and are a distance d apart.
o As shown earlier in the notes, each current will generate a magnetic field
at the location of the other wire; i.e., there is a magnetic field at wire 2 due
to the current through wire 1, and vice versa.
Magnetism Notes
Physics
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Bradshaw 04-05
Ed. 2010
Name _________________________________________________
Period _______
o When a current flows through a magnetic field, as we have seen, there will
be a magnetic force. So, each wire feels a magnetic force due to the
presence of the other. The magnitude of the magnetic force that each wire
feels is
FB = 0I1I2L
[2d]
o The direction of this force is easy to remember: when the currents flow in
the same direction, the force is attractive; when the currents flow in
opposite directions, the force is repulsive.
o Often, the length of wire will be divided out of the previous equation,
giving an expression for the Force per unit Length acting on a wire; this
is in many cases a more useful expression:
FB = 0I1I2
L [2d]
o **It is from this expression that we get our modern definition of the unit
of current; the Ampere. The definition states that 1 A of current is
defined as the amount of current flowing through two long parallel
wires 1 m apart that results in a force of exactly 2 E-7 N/m of length in
the wire.
Magnetism Notes
Physics
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Bradshaw 04-05
Ed. 2010