Magnets and Magnetic Fields
Electric Currents produce Magnetic Fields
Magnetic Force on current carrying wires and moving Charged particles.
Picture shows a small bar
magnet sitting in the
Earth’s magnetic field
Alnico magnets
(Iron + Al +Ni + Co)
10%
18%
Ceramic (ferrite) magnets
Fe2O3 or Fe2O4 + other element
12%
Ampère’s Law
Solenoids &
Electromagnets
Mass Spectrometer
Torque & Magnetic Moment
Magnetic materials
20.1 Magnets and Magnetic Fields
Magnets have two poles (ends): North and South
A bar magnet is a magnetic dipole
Neodymium Iron
Boron (Nd2Fe14B)
magnets
‘singing’ magnets
20.1 Magnets and Magnetic Fields
Magnetic fields can be visualized
using magnetic field lines, which
are always closed loops.
The Earth’s magnetic field is similar
to that of a bar magnet.
When a magnet is cut in half, TWO
smaller magnets are produced.
A bar magnet
1 magnetic dipole
is a magnetic dipole
2 magnetic dipoles
Like poles repel
Unlike poles attract.
No magnetic monopoles*
are found in nature
*a single north or south pole
20.1 Magnets and Magnetic Fields
The field between two wide poles is nearly uniform.
Field lines emerge from the North pole and
enter the South pole.
They continue through the material.
They do not start or end at a single point.
The Earth’s “North Pole” is
really a south magnetic pole.
The north end of a magnet (e.g.
compass) is attracted to it.
20.2 Electric Currents Produce Magnetic Fields
What do we know about magnetism?
Magnetism is associated with charges in motion (currents)
e.g. tiny currents in the atoms of magnetic materials or
macroscopic currents in the windings of an electromagnet.
Magnetic Field lines are parallel
and evenly spaced here
– similar to the electric field inside
a capacitor.
Magnetic field, B is measured in Tesla, T
A static charge has an E
field associated with it.
1 T = 1 N / A m.
Another unit sometimes used is the gauss (G). 1 G = 10-4 T.
Earth’s magnetic field ~ 0.5 G
A moving charge has
both an E and B field
associated with it.
v
B field associated with
slowly moving (+) charge
above picture agrees with RHR-1
(next slide)
1
Question
20.5 Magnetic Field Due to a Long Straight Wire
The magnitude of the magnetic field around a
long thin current carrying wire is inversely
proportional to the distance from the wire:
RHR-1
Two parallel wires are 10 cm apart and carry 5.0 A and 7.0 A, in opposite directions.
What is the magnitude of magnetic field midway between the wires?
1.
2.
3.
(20-6)
4.8 × 10-5 T
8.0 × 10-6 T
2.4 × 10-5 T
I1 (out)
I2 (in)
5.0 cm 5.0 cm
7A
5A
µ0 is called the permeability of free
space, and has the value:
µ0 = 4π
π × 10-7 T m / A
(aka “magnetic constant”)
For several currents, add the components of
magnetic field using vector addition
Direction of the field
is given by the 1st
right-hand rule.
The currents in these wires have the same magnitude, but
opposite directions. P is the same distance from both wires.
What is the direction of the magnetic field at P ?
A current loop acts like a “magnetic dipole” (magnet)
If a long thin current carrying wire is bent into a loop…
It LOOKS LIKE A BAR MAGNET!
P
I
1.
2.
3.
4.
S
I
I
N
UP
DOWN
RIGHT
LEFT
Direction of the field
is again given by
RHR-1
20.3 Force on an Electric Current in a Magnetic Field
A magnet exerts a force on a current-carrying wire.
Direction of the force is given
by the 2nd right-hand rule.
RHR-2
20.3 Force on an Electric current in a Magnetic Field
Magnitude of the force on the wire depends on
the current, the length of the wire in the B field, I
the magnetic field, and its orientation.
l
N
θ
S
(20-1)
between I and B
10A flows through a 5 cm long wire. 2 cm of the wire sits in
a 0.6 T magnet (see above). The wire is at 70o to the B field
Note on vector notation,
or
= INTO page
or
= OUT of page
Force is always
⊥ to I and B
What is the magnetic
force on the wire?
1.
2.
3.
4.
0.1 N into page
0.3 N into page
0.1 N out of page
0.3 N out of page
2
20.6 Force between Two Parallel Wires
20.4 Force on an Electric Charge Moving in a Magnetic Field
Two parallel currents exert a force on each other.
B1
Magnetic field from I1 at
position of wire 2 is:
d
The magnetic force on
a length l2 of wire 2 is:
A magnet also exerts a force
on a moving point charge
RHR-3
(on + charge)
(20-3)
‫ܨ‬റ 2
Between
v and B
(20-7)
Wire 1
Force is always
⊥ to v and B
antiparallel
currents
repel.
Parallel
currents
attract;
For a negative charge,
reverse the direction of F
20.4 Force on an Electric Charge Moving in a Magnetic Field
If a charged particle (mass m, charge q, speed v)
moves perpendicular to a uniform magnetic field
(B), its path will be a circle of radius r.
r=
Direction is given by the 3rd
right-hand rule.
At one moment in time, a proton (m = 1.67 x 10-27 kg) is moving
at 4.0 x 105 m/s downwards in a uniform 0.008 T magnetic field,
which points into the page.
Describe the path of the proton
It moves,
1. CW in a circle of radius 6.1 mm
2. CW in a circle of radius 3.5 mm
3. CCW in a circle of radius 52 cm
4. In a straight line at the same speed
mv
qB
Does this magnetic field do WORK on the charged particle?
20.4 Force on Electric Charge Moving in a Magnetic Field
What if the proton was moving directly OUT of the page?
Summary of Right hand rules
Magnetic field around
a current
RHR-1
If the velocity is NOT perpendicular to the
field, the charged particle moves in a
helical (spiral) path.
Force on a current due to a
magnetic field
RHR-2
Force on a charge (+q) due
to a magnetic field
RHR-3
(on +
charge)
࢜
This effect gives rise to
the Aurora Borealis
I or v
F
Problem solving: things to remember
(on I or
1 F is perpendicular to B and I (or v).
(+) charge)
2 Right-hand rule determines the direction of F.
3 Equations in this chapter give the magnitude of F.
B
Force
Force
⊥ to v and B
⊥ to I and B
Thumb points in
direction of I.
Fingers point in direction of I, Fingers point in direction of
particle’s velocity, v,
Fingers wrap around
then bend along B.
wire and point in
then bend along B.
Thumb gives direction of force
Thumb gives direction of force
direction of B
3
20.7 Solenoids and Electromagnets
Question...
Steady current flows UP a wire. A POSITIVE point
charge moves away from the wire at constant speed, v.
In which direction does the magnetic
force act on the positive charge?
v
1.
2.
3.
4.
5.
6.
I
A solenoid is a long coil of
wire. If it is tightly wrapped, the
magnetic field inside is almost
uniform.
B field inside a solenoid with
N loops:
UP
DOWN
RIGHT
LEFT
INTO PAGE
OUT OF PAGE
Electromagnets:
If a piece of iron (iron core)
is placed inside the
solenoid, the magnetic field
greatly increases.
Why ?
The iron becomes
magnetized in the field and
its magnetic field adds to
that of the solenoid.
(20-8)
Electromagnets have many
practical applications.
again, it looks just like a bar magnet
20.8 Ampère’s Law
20.8 Ampère’s Law
Ampère’s law is used to calculate the magnetic field in
situations with a high degree of symmetry.
e.g. Magnetic field due to a long straight wire
(Ampere’s Law)
It relates the magnetic field around a
closed path to the total current through
the surface bounded by the path.
For circular path around the wire:
B// = B for any segment of the path. And,
(20-9)
ΣB||∆l = BΣ∆l = B(2πr) = µ0I
Component of B parallel
to each segment
B = µ0I
2πr
(derivations using Ampere’s Law
will not be in the exam)
20.9 Torque on a Current Loop
‫ ܯ‬is a vector that points along the
coil axis, along the field lines.
It has magnitude:
20.9 Torque on a Current Loop
Area, A
Each current loop has a Magnetic
Moment (‫ )ܯ‬associated with it.
M
I
(20-11)
(same as 20-6)
The torque is maximum when ‫ ܯ‬is perpendicular to ‫ܤ‬
and its zero when ‫ ܯ‬is parallel to ‫ܤ‬
‫ܯ‬
N loops
‫ܯ‬
θ
‫ܯ‬
‫ܯ‬
If the current loop is placed in a
magnetic field it may experience a
Torque (turning force) of magnitude:
θ = 90o
Max torque
θ = 0o
Zero torque
(20-10)
between
ࡹ and ࡮
Current loops, solenoids and bar magnets (if free to move)
all want to line up with their axis parallel to the field eg. a compass.
4
Question...
20.11 Mass Spectrometer
A single square loop of wire (area = 0.50 m2) is placed in a 0.6 T
magnetic field. A current of 3.0 A flows in the coil, as shown.
1. Find the speed of the ions
I=3A
For certain values of E and B the
forces on an ion balance and it
passes through undeflected.
60ο
B = 0.6 T
Which statement about the torque is TRUE?
1.
2.
3.
4.
5.
There is ZERO torque on the loop.
τ = 0.45 Nm and the loop turns CCW.
τ = 0.45 Nm and the loop turns CW.
τ = 0.78 Nm and the loop turns CCW.
τ = 0.78 Nm and the loop turns CW
E and B are ⊥ here.
‫ܨ‬ா = ‫ܨ‬஻ so ‫ܧ = ݒ‬/‫ܤ‬
Paramagnetism
Diamagnetism
Ion
sourc
e
2. Determine their mass.
All ions passing through s2 have speed, v
Knowing their speed and
the radius of their path, r
in a 2nd uniform field, B′′
allows us to determine the
mass of the ions,
݉=
‫ܤݍ‬ᇱ ‫ݎܤ‬
‫ܧ‬
Typically, charge
on an ion, q = e
Summary of Chapter 20
Magnetic materials
Ferromagnetism is a property of iron and a few other materials.
Ferromagnetic materials contain tiny domains; each domain
acts like a small magnet with a N and S pole
If the domains are preferentially aligned in
one direction the material can be made
into a permanent magnet
- uses the motion of ions in a B
field to determine their mass
• Magnets have north and south poles
• Like poles repel, unlike attract
• B field near a long, straight
current-carrying wire:
• B field exerts a force
on an electric current:
• Unit of magnetic field: tesla
• Electric currents produce
magnetic fields
A charge moving at
constant speed, ⊥ to
a uniform B field
moves in a circle
• B field exerts a force
on a moving charge:
r=
• Parallel currents attract; antiparallel currents repel
Atoms in paramagnets have randomly
orientated permanent magnetic dipoles.
They become aligned in a magnetic
field and are attracted to a magnet
When a diamagnet is placed
in a magnetic field the atoms
gain a magnetic dipole that
opposes the external field.
• Magnetic field
inside a solenoid:
mv
qB
• Ampère’s law:
• Torque on a
current loop:
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