A moving charge produces magnetic field There are two basic ideas in our introductory study of magnetism FIRST THINGS FIRST THEIR MAJESTY THEMSELVES MAGNETS The ancient Greeks originally those near the city of Magnesia and also the early Chinese knew about strange and rare stones ID: 760224
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Slide1
Magnetism
● An electric charge experiences a magnetic force when moving in magnetic field.
● A moving charge produces magnetic field
There are two basic ideas in our introductory study of magnetism.
FIRST THINGS FIRST: THEIR MAJESTY THEMSELVES - MAGNETS
Slide2The 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).
http://www-spof.gsfc.nasa.gov/Education/Imagnet.html
Slide3Experience: 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.
Slide4Magnets are Cool!
North Pole and South PoleUnlikes AttractLikes Repel
NS
SN
N
S
NS
Slide5Contrary 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!
N
S
S
S
N
N
S
N
S
N
S
N
S
N
Magnetic monopoles have never been detected.
Slide6magnetically-levitated trains…
http://www.scicymru.info/sciwales/indexphpsectionchoose_scienceuser_typePupilpage_id11696languageEnglish.htm
Slide7Earth’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.
Earth's magnetic
field has flipped many times over the last billion years.
Don’t freak out:
N
S
N
S
Slide8No 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)
Slide9The Magnetic Field
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.
We’ll give definition of mag. field intensity B soon. You can peek – couple of slides later.
A magnetic field is said to exist at a point if a compassneedle placed there experiences a force.
Slide10Field 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
Slide11Magnetic Field Lines
Magnetic Field LinesArrows give direction Density gives strengthLooks like dipole!
Slide12Question
Which diagram shows the correct field lines of a bar magnet?(1) (2) (3)
Field lines do NOT stop abruptly
Field lines are continuous
Slide13Convention for direction:
x
x
x
x
x
x
x
INTO Page
••••••••••••• OUT of Page
Slide14The 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
.
F = qvB sin q
F plane of v and B
The Magnetic Field – strength and direction
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
(
q
is the angle between the charge’s velocity and the magnetic field)
Slide15charge q moving with velocity v in the mag. field B
v
B
q
.
The
direction
of the magnetic force is given by the Right-Hand Rule One – RHR 1
►
Point fingers in v (or I) direction
F
positive charge
F
negative charge
►
Curle
fingers as if rotating
vector v (current I) into B.
►
Thumb is in the direction of the force.
● For negative charge force is
in the opposite direction
F =
qvB
sin
q
F is perpendicular
to the plane of v and B
Slide16Slide17The electric force: Felec = Eq
The magnetic force: Fmag = qvB sin q
Charge q in elec. field E and mag. field B
is always parallel to the direction of the electric field. acts on a charged particle independent of the particle’s velocity. does the work when moving charge: The work, W = Fel d cosθ1, is converted into kinetic energy which is, in the case of conductors, transferred to thermal energy through collisions with the lattice ions causing increased amplitude of vibrations seen as rise in temperature.
is always perpendicular to the direction of the magnetic field acts on a charged particle only when the particle is in motion (F=0 if v=0), and only if v and B do not point in the same or opposite direction (sin 00 = sin 1800 = 0). Force is perpendicular to the direction of the motion, so the work done by magnetic force is zero. W = Fmagd cosq1 = 0 (cos 900 = 0). W = ΔKE = 0 Hence change in kinetic energy of the charge is 0, and that means that mag. force can not change the speed of the charge. Magnetic force can only change direction of the velocity, but it doesn’t change the speed of the particle.
In the presence of magnetic field, the moving charged particle is deflected (dotted lines)
B
v
v
F
F
CLICK
θ
1
is angle between F and direction of motion (v and d)
Slide18We define the magnitude of the magnetic field by measuring the force on a moving charge:
v
B
q
The SI unit of magnetic field is the Tesla (T),
named after
Nikola Tesla
, a Croatian physicist.
1 T = 1 N
·
s/(
C
·
m
)
Slide19Question?
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 Same
B
1
2
3
F = q v B sin
q
Slide20Question?
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
1
2
3
B(fingers) points right.
Velocity points in two different directions.
RHR determines force direction - different!
F = q v B sin
q
Slide21Two important applications of the Lorentz force are the trajectory of a charged particle in a uniform magnetic field and 2) the force on a current-carrying conductor.
Examples of the Lorentz Force
Slide22Motion of charge q in B Fields
Centripetal force: F
c
= mac = m v2/R in this case Fc is mag. force, so qvB = m v2/R sin θ = 1
positive charge
Force is perpendicular to B,vB does no work! (W = F d cos θ1 )Speed is constant (W = Δ KE )Circular motion
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
http://www.sr.bham.ac.uk/xmm/fmc4.html
massive or fast charges – large circles
large charges and/or large B – small circles
R
F
v
F
F
F
F
F
Slide23Question
What is the speed of the particle in chamber 2?1) v2 < v12) v2 = v13) v2 > v1
1
2
v = 75 m/s
q = +25 mC
Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v
1
= 75 m/s up, and follows the dashed trajectory.
43
Magnetic force is always perpendicular to velocity, so it changes direction, not speed of particle.
Slide24Question
Compare the magnitude of the magnetic field in chambers 1 and 21) B1 > B22) B1 = B2.3) B1 < B2
1
2
v = 75 m/s
q = +25 mC
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.
Larger B, greater force, smaller R
Slide25Question
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 mC2) Q = 25 mC3) Q = 50 mC
1
2
v = 75 m/s
q = ?? mC
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.
If both mass and charge double there is no change in R
Slide262) 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:
F = ILB
sin
q
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!
Slide27Direction 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.
Slide28What is the direction of the force on section a-b?
force is zeroout of the page into the page
Here = 0.
A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides ab and cd.
B
Question
What is the direction of the force on section
b-c
of the wire?
force is zero
out of the page
into the page
Force on
c-d
is Zero!
Force on
a-d:
out of the page.
I
d
c
a
b
Slide29Net force on loop is
zero
out of the page
into the page
Look from here
a
b
c
d
F
F
I
d
c
a
b
•
F
X
F
Will the loop move?
Yes
No
But the torque is not zero!
ROTATION
Slide30A MOVING CHARGE PRODUCES A MAGNETIC FIELD
1820’s: Hans Oerstad discovers electromagnetism with his famous “compass and current - carrying wire” experiments (by accident)
Slide31Currents Create B fields - Ampere’s Law
r = distance from wire
Magnitude:
Lines of
B
r
B
Current
I
OUT
Direction: RHR 2
T
humb in direction of current, fingers curl around current indicating direction of magnetic field
B decreases
as
m
0
=
4
p
10
-7
Tm/A
Slide32x x x x
x x x x
x x x x
x
x
x x
x x x x
●
● ● ●
●
● ● ●
● ● ● ●
● ● ● ●
● ● ● ●
I
x x x
x x x
x
x
x
x x x
x x x
●
●
●
●
● ●
● ● ●
● ● ●
● ● ●
I
B decreases as
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.
When indicating direction of B by crosses and dots we always draw it like this.
Slide33Many factories use industrial robots to carry materials or parts around. One type of robot follows a current-carrying cable buried in the floor by using special sensors to detect the magnetic field around the cable.
Slide34v
•
B
same
v and B are normal in both cases: sin
θ
= 1
A long straight wire is carrying current from left to right. Near the wire is a charge
q
(
-
) with velocity
v
I
v
a)
r
q
•
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)
q
•
r
b)
F
F
F has different directions
same
F = qvB
Slide35Example:
A long straight wire carrying a current of I = 3.0 A. A particle of charge q = 6.5 mC 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.
►
A charge moving through this magnetic field experiences a magnetic force:
F = qvB sin
q
►
Current generates a magnetic field in the space around the wire.
(q = 90
0
)
F = 2.2x10
-8
N
direction: predicted by RHR-1- radially inward toward the wire:
Slide36Two long wires carry opposite currents I
What is the direction of the magnetic field above, and midway between the two wires carrying current?
●
Adding Magnetic Fields
1) Left
2) Right
3) Up
4) Down
5) Zero
B
x
I
I
Slide37Example:
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
B
another
I up
F
Conclusion: Currents in same direction attract!
x
►
Point fingers in v (or I) direction
►
Curle
fingers as if rotating
vector v (current I) into B.
► Thumb is in the direction of the force.
F
I
up
B
another
I down
F
Conclusion: Currents in opposite direction repel!
x
►
Point fingers in v (or I) direction
►
Curle
fingers as if rotating
vector v (current I) into B.
► Thumb is in the direction of the force.
F
Slide39Slide40What 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
Slide41What is the direction of the force on the midlle wire, due to the two others?
1) Left 2) Right 3) Up 4) Down 5) Zero
I
I
I
What is the direction of the force on the left, due to the two others?
I
I
I
1) Left
2) Right
3) Up
4) Down
5) Zero
Other way: 1. find magnetic field due the other two and then use RHR1
Slide42What is the direction of the force on the midlle wire, due to the two others?
1) Left 2) Right 3) Up 4) Down 5) Zero
I
2I
3I
What is the direction of the force on the midlle wire, due to the two others?
I
I
I
1) Left
2) Right
3) Up
4) Down
5) Zero
Slide43What is the direction of the magnetic field produced in the midlle between two wires?
1) Left 2) Right 3) Up 4) Down 5) Zero
I
I
I
What is the direction of the force on the left, due to the two others?
I
I
I
1) Left
2) Right
3) Up
4) Down
5) Zero
Other way: 1. find magnetic field due the other two and then use RHR1
Slide44Electric and Magnetic Field
Direction:
Opposites
Charges
Attract
Currents Repel
Electric Magnetic
Source: Charges Moving Charges
Act on: Charges Moving Charges
Magnitude: F = q E F = q v B sin
θ
Direction: Parallel to E Perpendicular to v,B
Slide45Solenoids
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=m0nIn = number of windings per unit length,I = current in windings
B
0 outside windings
Slide46Example 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?