magnetic fields. magnetic fields and forces a single magnetic pole has never been isolated magnetic...
TRANSCRIPT
Magnetic Fields
Magnetic Fields and Forces
• a single magnetic pole has never been isolated
• magnetic poles are always found in pairs
• Earth itself is a large permanent magnet
Magnetic Fields and Forces
Magnetic Fields and Forces
• We can represent the magnetic field ( ) by means of drawings with magnetic field lines
• We can define a magnetic field at some point in space in terms of the magnetic force that the field exerts on a charged particle moving with a velocity
• Magnetic poles exert attractive or repulsive forces on each other and that these forces vary as the inverse square of the distance between interacting poles
B
B
BF
v
Magnetic Fields and Forces
• The magnitude FB of the magnetic force exerted on the particle is proportional to the charge q and to the speed v of the particle
• The magnitude and direction of depend on the velocity of the particle and on the magnitude and direction of the magnetic field (Tesla, T=N.s/(C.m), in SI unit)
• When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero
BF
B
Magnetic Fields and Forces
BF qv B
sinBF qv B qvB
Magnetic Fields and Forces
Example #13Example #13
• An electron in a television picture tube moves toward the front of the tube with a speed of 8.0 x106 m/s along the x axis (see the figure). Surrounding the neck of the tube are coils of wire that create a magnetic field of magnitude 0.025 T, directed at an angle of 600 to the x axis and lying in the xy plane. Calculate the magnetic force on the electron.
Magnetic Force Acting on a Current-Carrying
Conductor
• The resultant force exerted by the field on the wire is the vector sum of the individual forces exerted on all the charged particles making up the current
Magnetic Force Acting on a Current-Carrying
Conductor
Magnetic Force Acting on a Current-Carrying
Conductor
Magnetic Force Acting on a Current-Carrying
Conductor
B dF q v B nAL
BF IL B
n : the number of charges per unit volume
Magnetic Force Acting on a Current-Carrying
Conductor
BdF Ids B
b
B
a
F I ds B
Magnetic Force Acting on a Current-Carrying
Conductor
• The magnetic force on a curved current-carrying wire in a uniform magnetic field is equal to that on a straight wire connecting the end points and carrying the same current
Magnetic Force Acting on a Current-Carrying
Conductor
• The net magnetic force acting on any closed current loop in a uniform magnetic field is zero
Quiz#3Quiz#3
• Rank the wires according to the magnitude of the magnetic force exerted on them, from greatest to least
Sources of the Magnetic Field
• The Biot–Savart Law
02
ˆ
4
I ds rdB
r
02
ˆ
4
I ds rB
r
0 : 4 x 10-7 T.m/A
Magnetic Field Surrounding a Thin, Straight Conductor
0
2
IB
a
Magnetic Field on the Axis of a Circular Current Loop
20
32 2 22
x
IRB
x R
0
2
IB
R
At x=0
If x>>R
20
32
IRB
x
Magnetic Field on the Axis of a Circular Current Loop
The Magnetic Force Between
Two Parallel Conductors
• Parallel conductors carrying currents in the same direction attract each other
• Parallel conductors carrying currents in opposite directions repel each other0 2 0 1 2
1 1 2 1 2 2
I I IF I lB I l l
a a
Ampère’s Law
Ampère’s Law• The line integral of around any closed
path equals 0I, where I is the total steady current passing through any surface bounded by the closed path
sdB
002
2
IB ds B ds r I
r
Quiz#4Quiz#4
• Rank the magnitudes of for the closed paths in the figure from least to greatest
B ds
The Magnetic Field of a Solenoid
• A solenoid is a long wire wound in the form of a helix
The Magnetic Field of a Solenoid
The Magnetic Field of a Solenoid
1 1Path Path
B ds B ds B ds Bl
0B ds NI Bl
From Ampère’s Law
N: the number of turns
n: the number of turns per unit length
0B nI
Magnetic Flux
B B dA
Magnetic Flux
cosB BA
Gauss’s Law in Magnetism
• The net magnetic flux through any closed surface is always zero
The Magnetic Field of the Earth
Faraday’s Law of Faraday’s Law of InductionInduction
• An electric current can be induced in a secondary circuit by a changing magnetic field
• An induced emf is produced in the secondary circuit by the changing magnetic field
• The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit
Faraday’s Law of Faraday’s Law of InductionInduction
Bd
dt
BdNdt
a coil consisting of N loops all of the same area
Faraday’s Law of Faraday’s Law of InductionInduction
Lenz’s Law• The induced current in a loop is in
the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop
Lenz’s Law