Download Magnetic Fields and Forces

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 (B) by
means of drawings with magnetic field lines

• We can define a magnetic field B at some
point in space in terms of the magnetic
force FB that the field exerts on a charged
particle moving with a velocity v
• 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
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 FB depend
on the velocity of the particle and on the
magnitude
and direction of the magnetic

field B (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
Magnetic Fields and
Forces
FB  qv  B
FB  qv  B  qvB sin 
Magnetic Fields and
Forces
Example #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
FB  q  vd  B  nAL
FB  IL  B
n : the number of charges per unit volume
Magnetic Force Acting on a
Current-Carrying
Conductor
dFB  Ids  B
b
FB  I  ds  B
a
Magnetic Force Acting on a
Current-Carrying
Conductor
• The magnetic force
on a curved currentcarrying 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#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
0 I ds  rˆ
dB 
4 r 2
0 : 4 x 10-7 T.m/A
0 I ds  rˆ
B
2

4
r
Magnetic Field Surrounding
a Thin, Straight Conductor
0 I
B
2 a
Magnetic Field on the Axis
of a Circular Current Loop
Bx 
At x=0
B
0 I
2R
If x>>R
0 IR
2
2  x2  R
B
0 IR 2
2 x3
3
2 2

Magnetic Field on the Axis
of a Circular Current Loop
The Magnetic Force
Between
Two Parallel Conductors
 0 I 2  0 I1 I 2
F1  I1lB2  I1l 
l

 2 a  2 a
• Parallel conductors
carrying currents in
the same direction
attract each other
• Parallel conductors
carrying currents in
opposite directions
repel each other
Ampère’s Law
Ampère’s Law
 
• The line integral of B  ds around any closed
path equals 0I, where I is the total steady
current passing through any surface
bounded by the closed path
0 I
 B  ds  B  ds  2 r  2 r   0 I
Quiz#4
• Rank the magnitudes
of  B  ds for the closed
paths in the figure
from least to greatest
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
 B  ds  
B  ds  B
Path1

ds  Bl
Path1
From Ampère’s Law
 B  ds   NI  Bl
0
N: the number of turns
B  0 nI
n: the number of turns per unit length
Magnetic Flux
 B   B  dA
Magnetic Flux
 B  BA cos 
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
Induction
• 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
Induction
dB
 
dt
a coil consisting of
N loops all of the same area
dB
  N
dt
Faraday’s Law of
Induction
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