Transcript Magnetism: Overview

Magnetism: Overview
• I Magnetic field exists; how does it affect
matter ?
• II What is the origin of magnetic field ?
• III How are electric and magnetic fields
related ?
Magnetic field lines
• emerge from North poles
• enter at South poles
• Magnetic field (B) is
tangent to field lines
• There is a corollary to
electric field lines!
Lorentz Force Law
Both the electric field and magnetic field can be
defined from the Lorentz force law:
The electric force is straightforward, being in the
direction of the electric field if the charge q is positive,
but the direction of the magnetic part of the force is
given by the right hand rule.
It’s what came before QVC
• So in very basic terms the force exerted on a
particle is simply
F= qvB
Where F is the Force (newtons)
q is the charge (in coulombs)
v is the velocity
and B is the strength of the magnetic field (in Teslas= 1
newton*second / coulomb * meter))
Right Hand rule #2
Right Hand Rule #1
Right Hand Rule #1- in wire
Current (I) through a
wire produces a
magnetic field (B)
around the wire. The
field is oriented
according to the right
hand grip rule.
Force on a moving charge
• charge must be moving (no force if neutral)
• charge must cut across field lines as it moves (no
force if charge moves parallel to field)
• for a given speed, greatest force occurs when v is
perpendicular to B
• for a given direction, greater speed means greater
force
Units of B are Tesla (T)
F  qvBsin
Charge moving perpendicular to field
lines
Magnetic Force
• Force is perpendicular to velocity of particle
• Force is perpendicular to field B
• Since the force is acting at right angles to
the motion, it does no work, so it cannot
cause a particle to speed up or slow down.
Trajectories
When moving in a uniform field, the path of a charge depends in a simple way on its
direction with respect to the field. There are three cases:
1)
2)

v


B  F  0  Uniform motion (no acceleration)
 
v  B  F  qvB
This leads to uniform
circular motion
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
 v2 
mv
qvB  m   R 
qB
R
3) Both
vll and v present
This leads to a superposition of cases 1 and 2. What do you get when you
superpose circular motion perpendicular to the field with uniform motion along
the field?
Helix, with axis along field
Even if the field is not uniform, charges will tend to circle around the local field lines
as they drift along these same lines
Solar Wind and the Earth Field
Exercise: An electron is accelerated through a potential difference of 100 V and then enters a
region of magnetic field .1 T, moving at right angles to the field. Find the radius of the circular
orbit.
KE   PE
1 2
2qV
m v  qV  v 
2
m


2 1.6 x1019 100
6 m
v
 5.96x10
31
9 x10
s

31

6
m v 9 x10 5.96x10
R

19
qB
1.6 x10 .1

4
R  3.35x10 m
Force on current
The moving charges within a wire are an easily accessible example of the
magnetic force.
Since we usually describe these charges in terms of their associated electric
current, it makes sense to “rewrite” the magnetic force in terms of circuit
parameters.
X
x
x
x
x
x
x
v
Assume
there are N
charges in L
X
x
x
x
x
x
L
F  qvB  Ftotal  NqvB
Nq Nq Nqv
i


t
L/v
L
 F  iLB
x
B
Origin of magnetic field
• What can experience an
electric field?
charge
• What is the origin of the
electric field?
charges
• What can experience a
magnetic field?
Moving charge
• What is the origin of the
magnetic field?
Moving charges
Electric currents are a readily available source of moving charges.
Field due to a long wire
k I
B
R
k   2 x10 7
T m
A
•
•
Direction determined by RHR #2:
Thumb along current, then fingers
curl along field lines
OO
Exercise: Find the magnetic field 10 cm from a wire carrying a current of 20 A.
k I
20
B  2 x10 7  4 x10 5 T
R
.1
Ferromagnetism
If moving charges are the source of magnetic fields, what are the moving charges in everyday
iron magnets?
1) Orbital motion of electrons
While this motion does create magnetic fields, over a scale much larger than an
individual atom, it will average out to zero since different atoms will have their electrons
circulating in different directions.
2) Spin: electrons have an intrinsic spin; this motion will create magnetic fields also.
Once again, over a large scale, these fields tend to cancel, except for certain materials.
In some materials there is a residual interaction between the spinning electrons that tends to
make them spin in same direction, and this causes the magnetic fields they create to add up,
not cancel.
These materials are said to be “ferromagnetic” and include iron, cobalt, nickel, and others.
The interaction between spinning electrons has a finite range, and one finds that the tendency
to line up is limited to a region large compared to atoms but still small compared to our
everyday scale.
These regions are called “domains”.
To actually make a magnet, one has to align the domains, perhaps with a large external field.
A species of marine bacteria that live in
the sediment at the bottom of the ocean
actually contain roughly 5-20 magnetic
particles aligned along the long axis of
the organism.
Should they be disturbed out of the
sediment, their internal magnet aligns
along the local earth field line and they
swim back down to the sediment.
In the northern hemisphere, the
organism has a south pole at its
anterior, while the opposite occurs in
the southern hemisphere.
A northern hemisphere organism
brought to the southern hemisphere
will swim to the surface!
http://www4.ncsu.edu/~rwchabay/emimovies/right-ha.html