Download The Magnetic Field

Magnetism
There are two basic ideas in our introductory study of magnetism.
● An electric charge experiences a magnetic force when moving in magnetic field.
● A moving charge produces magnetic field
FIRST THINGS FIRST: THEIR MAJESTY THEMSELVES - MAGNETS
http://www-spof.gsfc.nasa.gov/Education/Imagnet.html
The ancient Greeks, originally those near the city of Magnesia, and also the early
Chinese knew about strange and rare stones (possibly chunks of iron ore struck by
lightning) with the power to attract iron. A steel needle stroked with such a
"lodestone" became "magnetic" as well, and around 1000 the Chinese found that
such a needle, when freely suspended, pointed north-south - compass.
The magnetic compass soon spread to Europe. Columbus used it when he
crossed the Atlantic ocean, noting not only that the needle deviated slightly from
exact north (as indicated by the stars) but also that the deviation changed during the
voyage. Around 1600 William Gilbert, physician to Queen Elizabeth I of England,
proposed an explanation: the Earth itself was a giant magnet, with its magnetic
poles some distance away from its geographic ones (i.e. near the points defining
the axis around which the Earth turns).
Experience: compass needle rotating in the Earth’s magnetic field
Facts: every magnet, regardless of its shape, has two poles, called
north pole and south pole, which exert forces on each other in a
manner analogous to electrical charges. The force between like poles
is repulsive, and the force between opposite poles is attractive.
Magnets are Cool!

North Pole and South Pole
 Unlikes Attract
 Likes Repel
N
S
S
N
N
N
S
S
Contrary to the electric dipole, which we can pull apart and isolate + and – charge,
we can NEVER pull apart magnetic dipole. When we cut magnet in two we end up
with two smaller dipoles. If we keep on cutting, more magnets will be produced,
EACH with north and south pole.
Let’s Break A Magnet!
S
Magnetic monopoles have never
been detected.
S
SNSN
N
N S
N
SNSN
magnetically-levitated trains…
http://www.scicymru.info/sciwales/indexphp
sectionchoose_scienceuser_typePupilpage
_id11696languageEnglish.htm
Earth’s A Magnet!
The poles received their names because of the behavior of a magnet in the
presence of the Earth’s magnetic field. The pole of a magnetic needle that points
to the north of the Earth is called north pole. So, magnetic pole which is in the
geographic north is magnetically south pole.
Don’t freak out:
Earth's magnetic field has flipped many
times over the last billion years.
No Magnetic Charges


Magnetic Fields are created by moving electric charge!
Where is the moving charge?
Orbits of electrons about nuclei
Intrinsic “spin” of
electrons (more
important effect)
The Magnetic Field 𝑩
A magnetic field is said to exist at a point if a compass
needle placed there experiences a force.
We’ll give definition of mag. field intensity B soon.
You can peek – couple of slides later.
The direction of the magnetic field at any location is the direction in
which the north pole of the compass needle points at that location.
Field Lines of Bar Magnet
Magnetic field lines don’t start or stop.
There are no magnetic charges
(monopoles)
But don’t be confused if you see pictures on the right
Magnetic Field Lines
•
Magnetic Field Lines
– Arrows give direction
– Density gives strength
– Looks like dipole!
Question
Which diagram shows the
correct field lines of a bar
magnet?
(1)
(2)
(3)
Field lines are
continuous
Field lines do
NOT stop
abruptly
Convention for direction:
x x x x x x x INTO Page
•••••••••••••
OUT of Page
The Magnetic Field – strength and direction
The strength/magnitude of mag. field at any point we define in terms
of the force exerted on a charged particle moving with a velocity v
A charged particle moving in a magnetic field experiences a
(magnetic) force that is perpendicular to the particle’s velocity and,
surprisingly, to the magnetic field itself.
Lorentz Force Law, named after the Dutch physicist of the late 19th and early
20th century Hendrik Antoon Lorentz.
The magnitude of the magnetic force on a moving, charged particle is
F = qvB sin q
F
(q is the angle between the charge’s
velocity and the magnetic field)
plane of v and B
The direction of the magnetic force is given by the
Right-Hand Rule One – RHR 1
F
positive
charge
► Point fingers in v (or I) direction
► Curle fingers as if rotating
vector v (current I) into B.
B
► Thumb is in the direction of the force.
q
v
charge q moving
with velocity v in
the mag. field B
F
negative
charge
● For negative charge force is
in the opposite direction
F = qvB sin q
F is perpendicular to the
plane of v and B
Charge q in elec. field E and mag. field B
The electric force: Felec = Eq
The magnetic force: Fmag = qvB sin q
 is always parallel to the direction
 is always perpendicular to the direction of the
of the electric field.
magnetic field
 acts on a charged particle only when the
 acts on a charged particle
independent of the particle’s velocity.
particle is in motion (F=0 if v=0), and only
 does the work when moving charge:
if v and B do not point in the same or opposite
The work, W = Fel d cosθ1, is
direction (sin 00 = sin 1800 = 0).
converted into kinetic energy which is,  Force is perpendicular to the direction of the motion,
in the case of conductors, transferred to
so the work done by magnetic force is zero.
thermal energy through collisions with
W = Fmagd cosq1 = 0 (cos 900 = 0).
the lattice ions causing increased
W = ΔKE = 0
amplitude of vibrations seen as rise in
Hence change in kinetic energy of the charge is 0,
temperature.
and that means that mag. force can not change
the speed of the charge. Magnetic force can only
θ1 is angle between F and direction
change direction of the velocity, but it doesn’t
of motion (v and d)
change the speed of the particle.
v F
B
v
CLICK
F
In the presence of magnetic field, the moving
charged particle is deflected (dotted lines)
We define the magnitude of the magnetic field by measuring the force on a
moving charge:
F
B=
qv sin q
B
q
v
The SI unit of magnetic field is the Tesla (T), named after Nikola Tesla,
a Croatian physicist.
1 T = 1 N·s/(C·m)
N
Ns
=
m Cm
C
s
Question?
The three charges below have equal charge and speed,
but are traveling in different directions in a uniform
magnetic field.
Which particle experiences the greatest magnetic force?
1
2
3
3
2
1
Same
B
F = q v B sin q
Question?
The three charges below have equal charge and speed, but
are traveling in different directions in a uniform magnetic
field.
The force on particle 3 is in the same direction as the force on
particle 1.
1) True
2) False
B
F = q v B sin q
B(fingers) points right.
3
Velocity points in two
different directions.
2
RHR determines force
direction - different!
1
Examples of the Lorentz Force
Two important applications of the Lorentz force are
1) the trajectory of a charged particle in a uniform magnetic field and
2) the force on a current-carrying conductor.
Motion of charge q in B Fields
positive charge
Force is perpendicular to B,v
 B does no work! (W = F d cos θ1 )
 Speed is constant (W = Δ KE )
 Circular motion
x
x
xRx
x
x
x
x
x
x
x
x
x
x
x
x
F
x
x
x
x
x
Centripetal force: Fc = mac = m v2/R
x
x
x
x
F

x
x
x
in this case Fc is mag. force, so
x
x
x
x
x
x
x
x
x
x
x
x
x
x
qvB = m v2/R
sin θ = 1
mv
R=
qB
 massive or fast charges – large circles
 large charges and/or large B – small circles
http://www.sr.bham.ac.
uk/xmm/fmc4.html
Question
Each chamber has a unique magnetic field. A
positively charged particle enters chamber 1
with velocity v1= 75 m/s up, and follows the
dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the speed of the particle in chamber 2?
1) v2 < v1
2) v2 = v1
3) v2 > v1
Magnetic force is always perpendicular to velocity, so it changes direction,
not speed of particle.
43
Question
Each chamber has a unique magnetic field. A
positively charged particle enters chamber 1
with velocity 75 m/s up, and follows the
dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
Compare the magnitude of the magnetic field in
chambers 1 and 2
1) B1 > B2
2) B1 = B2.
3) B1 < B2
Larger B, greater force, smaller R
mv
R=
qB
Question
Each chamber has a unique magnetic field. A
positively charged particle enters chamber 1
with velocity 75 m/s up, and follows the
dashed trajectory.
2
1
v = 75 m/s
q = ?? mC
mv
R=
qB
A second particle with mass 2m enters the chamber
and follows the same path as the particle with mass
m and charge q=25 mC. What is its charge?
1) Q = 12.5 mC
2) Q = 25 mC
3) Q = 50 mC
If both mass and charge double there is no
change in R
2) Suppose that we have a piece of wire carrying charges
(again, we'll assume it's positive charges moving around). A
number of charges, Dq, moves a distance L in some duration of
time, Dt. The force acting on these charges is:
 
 Dq 
L
F = DqvB sinq = Dq
B sinq = 
LB sinq

Dt
 Dt 
F = ILB sinq
This new form of Lorentz law we call the MACROSCOPIC FORM of Lorentz
Force Law. We don't have to go down to the microscopic level and look at
individual charges and look at their individual speeds. All we have to do is look
at a wire, determine its length and the current it carries and we can tell the
magnetic force acting on that piece of wire!
Direction of the force:
Put your RIGHT hand fingers in the
direction of the conventional current. Curl
them towards the direction of the
magnetic field. Your thumb will point in
the direction of magnetic force.
Question
A rectangular loop of wire is carrying current as shown. There is a
uniform magnetic field parallel to the sides ab and cd.
c
d
B
What is the direction of
the force on section a-b?
force is zero
a
b
I
What is the direction of the force on section
b-c of the wire?
Here q = 0.
out of the page
into the page
Force on
c-d is Zero!
force is zero
out of the page
into the page
Force on a-d:
out of the page.
d
•
a
X
F
c
F
b
I
Look from here
F
c
d
a
Net force on loop is
Will the loop move?
zero
Yes
out of the page
No
into the page
b
But the torque is
not zero!
ROTATION
F
A MOVING CHARGE PRODUCES
A MAGNETIC FIELD

1820’s: Hans Oerstad discovers
electromagnetism with his famous
“compass and current - carrying
wire” experiments (by accident)
Currents Create B fields - Ampere’s Law
Magnitude:
0I
B=
2r
Direction: RHR 2
Thumb in direction
of current, fingers
curl around current
indicating direction
of magnetic field
r = distance from wire
 0 = 4
 10-7 Tm/A
B
1
B decreases as r
r
Current I OUT
Lines of B
When indicating direction of B
by crosses and dots we always
draw it like this.
I
●
●
●
●
x
x
x
x
●
●
●
●
x
x
x
x
●
●
●
●
x
x
x
x
●
●
●
●
x
x
x
x
●
●
●
●
x
x
x
x
I
1
B decreases as r
so the right way that indicates the
weaker magnetic field away from
current is this.
BUT!!!! we don’t do it, except when
we draw couple of circles.
●
●
●
x
x
x
●
●
●
x
x
x
●
●
●
x
x
x
●
●
●
x
x
x
●
●
●
x
x
x
Many factories use industrial robots to carry materials
or parts around. One type of robot follows a currentcarrying cable buried in the floor by using special
sensors to detect the magnetic field around the cable.
q
v
•
a)
F
B•
v
q
•
b)
r
F
r
I
A long straight wire is carrying current from left to right. Near
the wire is a charge q (-) with velocity v
Compare magnetic force on q in (a) vs. (b)
a) has the larger force
b) has the larger force
c) force is the same for (a) and (b)
same B =
0I
2r
v and B are normal in both cases: sinθ= 1
same
F = qvB
F has different directions
Example:
A long straight wire carrying a current of I = 3.0 A.
A particle of charge q = 6.5 C is moving parallel to the wire at a distance
of r = 0.050 m from it; the speed of the particle is v = 280 m/s.
Determine the magnitude and direction of the magnetic force exerted on
the moving charge by the current in the wire.
0 I
B=
2 r
► Current generates a magnetic
field in the space around the wire.
► A charge moving through this magnetic field
experiences a magnetic force: F = qvB sinq
0 I
F = qv
2 r
q = 900
F = 2.2x10-8 N
direction: predicted by RHR-1- radially inward toward the wire:
Adding Magnetic Fields
Two long wires carry opposite currents I
B
●
I
x
I
What is the direction of the magnetic field above, and midway
between the two wires carrying current?
1) Left 2) Right
3) Up
4) Down 5) Zero
Example:
Two current-carrying wires exert magnetic forces on one another
We already saw that if we put a current carrying wire into a magnetic
field it will feel a force....so what will happen when we put two current
carrying wires together!?!?! One will create magnetic field that the other
will feel a force from, and vice versa! Let us see what is going on.
Force between wires carrying current
I up
another I up
B
F
Fx
► Curle fingers as if rotating
vector
v (current
I) into B.
Conclusion:
Currents
in same
direction
attract!is in the direction of the force.
► Thumb
another I down
I up
F
► Point fingers in v (or I) direction
B
xF
► Point fingers in v (or I) direction
► Curle fingers as if rotating
vector v (current I) into B.
Conclusion: Currents in opposite
direction
repel!is in the direction of the force.
► Thumb
0 I1
B=
2 d
0 I1
F = BI 2 L =
I2L
2 d
0 I1 I 2
F
Force per unit length,
=
L
2 d
What is the direction of the force on the top
wire, due to the two below?
1) Left 2) Right
3) Up
4) Down 5) Zero
What is the direction of the force
on the midlle wire, due to the two
others?
I
1) Left
I
2) Right
4) Down 5) Zero
I
3) Up
What is the direction of the force
on the left, due to the two others?
I
1) Left
I
2) Right
I
3) Up
4) Down 5) Zero
Other way: 1. find magnetic field due the other two
and then use RHR1
What is the direction of the force
on the midlle wire, due to the two
others?
I
1) Left
2I
2) Right
4) Down 5) Zero
3I
3) Up
What is the direction of the force
on the midlle wire, due to the two
others?
I
1) Left
I
2) Right
4) Down 5) Zero
I
3) Up
What is the direction of the
magnetic field produced in the
midlle between two wires?
I
1) Left
I
2) Right
4) Down 5) Zero
I
3) Up
What is the direction of the force
on the left, due to the two others?
I
1) Left
I
2) Right
I
3) Up
4) Down 5) Zero
Other way: 1. find magnetic field due the other two
and then use RHR1
Electric and Magnetic Field
Electric
Source:
Charges
Act on:
Charges
Magnitude: F = q E
Direction:
Parallel to E
Magnetic
Moving Charges
Moving Charges
F = q v B sin θ
Perpendicular to v,B
Direction:
Opposites Charges Attract
Currents Repel
Solenoids
A solenoid consists of
several current loops
stacked together.
In the limit of a very long
solenoid, the magnetic
field inside is very
uniform:
B=m0nI
n = number of windings
per unit length,
I = current in windings
B  0 outside windings
Example Problem 1
A solenoid that is 75 cm long produces a magnetic field of 1.3 T within its core
when it carries a current of 8.4 A. How many turns of wire are contained in
this solenoid?