the magnetic field
DESCRIPTION
The Magnetic Field. Chapter 30. Magnetic Forces. Magnetic Force - A force present when an electric charge is in motion. A moving charge is said to produce a magnetic field . Magnetic fields exert forces on moving charges. Magnetic Fields. Represented by field lines . By definition: - PowerPoint PPT PresentationTRANSCRIPT
1
The Magnetic Field
Chapter 30
2
Magnetic Forces
• Magnetic Force - A force present when an electric charge is in motion.
• A moving charge is said to produce a magnetic field .
• Magnetic fields exert forces on moving charges.
3
Magnetic Fields
• Represented by field lines .• By definition:
• or more commonly:
• Where q is the angle between v and B.
B =F
Qvsinq
F = qvBsinq
F = qv B
4
Magnetic Field Units
• Standard Unit = Tesla (T)
• 1 T = 1 N/A•m
• 1 T = 104 gauss
5
Force on Moving Charges• The diagram below shows a uniform
magnetic field with several charges in motion.
+ +
+ – x
vv
vv
6
Force on Moving Charges
• The magnitude of the force on each charge can be found by qv X B or qvBsinq.
• The direction of the force is found by a right hand rule.
7
Right Hand Rule
• 1) Place your fingers in the direction of the velocity.
• 2) Curl your fingers toward the direction of the field. You might need to turn your hand.
• 3) Your thumb points in the direction of the force.
8
Direction of Force
+ +
+ – x
vv
vv
F = 0
F
F
F
9
Magnetic Field Lines
• NOT lines of force.• Force on charges is not in the direction of
the magnetic field.• Force is always perpendicular to the
velocity of the charge.• Force is always perpendicular to the
magnetic field.• RHR & LHR
10
Permanent Magnets• Magnetic field lines point away from north
poles• and toward south poles.
11
Magnetic Flux
• The amount of a magnetic field passing through a given area.
• Proportional to the number of magnetic field lines which pass through an area.
B = BA cosq = B • AB =
B d A
12
Magnetic Flux
Maximum Flux
No Flux
A
A
A
13
Flux Units
• Weber• 1 Wb = 1 T/m2
14
Gauss's Law for Magnetism
• The magnetic flux through any closed surface must be zero.
N S BdA 0
15
Example
• Exercise 4
16
homework
• E 1, 2, 7
17
Motion of Charges in a Magnetic Field
• Two possible paths can result for the motion of the charge:
• 1) If vo is perpendicular to B, a circular path will result.
• 2) If vo is not perpendicular to B, the charge will travel in a spiral path.
18
vo perpendicular to B
19
vo at an angle to B
20
Magnetic Bottle
21
Van Allen Belts
22
Motion of Charges• As a charge circles or spirals in a magnetic
field, the radius of its path is dependent on the perpendicular component of its velocity.
FB = Fc
QvB =mv2
r
r =mv
QB
T =2rv
=2mqB
vr
qBm
23
Mass Spectrometer
r =mv
QB
24
Velocity Selector
• Only allows charges with a specific velocity to pass through undeflected.
• FB is opposite of FE
• E is perpendicular to B
25
Velocity Selector
+ v
– – – – – – – – – –
+ + + + + + + + + +
•
•
•
••
•FE
FB
26
Velocity Selector
• For a specific value of v, the electric force and the magnetic force will be equal to each other and opposite in direction.
• FB = FE
• qvB = qE• vB = E
27
Current-Carrying Wire• Since a current is moving charges, a
current-carrying wire experiences a force in a magnetic field. (B into screen)
X X X X X X X X
X X X X X X X X
F
28
Magnitude of Force
F QvBsinq Q Itv Lt
Qv ItLt
IL
F ILBsinq F IL B
29
Example
• Exercise 14
30
homework
• E 19, 20
31
Sources of Magnetic Fields
Chapter 31
32
Long, straight wire
B =oI2r
o is equal to 4 x 10–7 T•m/A.
33
Current Carrying Wire
• Shape of the field is circular.• Concentric circles• The direction is given a Right Hand Rule:
– Thumb in the direction of the current.– Curl your fingers and they give the direction of
the field.
34
Moving Charge
+ • v
35
Wire
I
• • • • • • • • •
x x x x x x x x x
B
I
36
Parallel conductors
• Each creates a magnetic field that produces a force on the other
• Can calculate force per unit length
• To find direction, use both right hand rules
rII
lF
2
0
37
Definition of Ampere
• Comes from force exerted by two parallel conductors
• 1 A is the current necessary in each conductor (if 1 m apart) to produce a force of 2 x 10-7 N.
38
Field of a circular loop or coil
• At center of loop
• Direction found with right hand rule – like current in straight wire
RNIB
20
39
Field of a Solenoid• Long Spring-like Coil• Uniform field in the interior:
B = onI
B oNL
I
40
Examples
• Exercises 1 and 7
41
homework
• E 2, 6, 10, 12
42
Ampere’s Law
• Like Gauss’s law
encId 0sB
Iencparallel IsB 0
43
Long straight wire
I
rIB
IrB
2
2
0
0
encparallel IsB 0
44
Example• A wire has a radius of R and carries a current I that
is uniformly distributed across its area.• Determine how to calculate the magnitude of the
magnetic field inside and outside the conductor.
45
Inside• The current inside a circle of radius r would
be a fraction of the total current.• Same ratio as areas.• With total current, I:
Rr
B2r oI r2
R2
B oIr
2R2
46
Outside• A circle of radius r, where r > R, encloses
all the current.
B oI2rR
r
47
Example
• Determine the field inside a solenoid
lengthturns
n
48
Solenoid• Vertical sides – zero
because B is perpendicular to sides
• Side outside solenoid – if it is far away from the solenoid, B is zero
nLIBL 0
nIB 0
49
Paramagnetic materials
• Can become magnetized• An external magnetic field causes atoms to
line up so their currents add to the external field
50
Ferromagnetic materials
• Atomic currents line up even when no external field is present
• Permanent magnets
51
Electromagnets
52
homework
• E 24-26