Download Jonti`s first lecture (Magnetism)

PHYSICS 1B
Today’s lecture:
Magnetism
The Magnetic Field, B
Magnetic Forces
and
Motion in a Uniform Magnetic Field
Electricity & Magnetism
20/08/2013
PHYSICS 1B – Magnetism
A Brief History of Magnetism…
13th Century BC
Records show that the Chinese used a compass
with a magnetic needle, which is thought to have
been an invention of either Arabic or Indian origin.
800 BC
The Greeks discovered that the mineral magnetite
(Fe3O4) attracts piece of iron.
Electricity & Magnetism – Magnetism
Lecture 7, 04/12/2012
PHYSICS 1B – Magnetism
A Brief History of Magnetism…
1269
Pierre de Maricourt found that the direction of a
needle near a spherical natural magnet formed
lines that encircled the sphere.
Those lines also passed through two points
diametrically opposed to each other.
He called those points “poles”
1600
William Gilbert published the results of his
experiments with magnetism, suggesting the Earth
itself was a large, permanent magnet.
Electricity & Magnetism – Magnetism
Lecture 7, 04/12/2012
PHYSICS 1B – Magnetism
A Brief History of Magnetism…
1750
Experiments show that magnetic poles exert
attractive or repulsive forces on each other.
1819
Hans Christian Oersted observed that an electric
current deflected a compass needle during a
physics demonstration.
This revealed that there is a relationship between
electricity and magnetism!
Electricity & Magnetism – Magnetism
Lecture 7, 04/12/2012
PHYSICS 1B – Magnetism
Magnetic Poles
Every magnet, regardless of its shape, has two poles.
We call these the north and south poles.
Poles exert forces on each other, in much the same way that electric charges
exert forces on each other.
Like poles (and like charges) repel one another – i.e. N-N or S-S
Unlike poles attract each other – i.e. N-S
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Poles
The poles received their names due to the way a magnet behaves in the Earth’s
magnetic field.
If a bar magnet is suspended so that it can move freely, it will rotate.
The magnetic north pole will point towards the Earth’s north geographic pole
Which, a little perversely, means that the Earth’s north geographic pole is a
magnetic south pole, and the Earth’s south geographic pole is a magnetic north
pole!
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Poles, final
The force between two poles varies as the inverse square of the distance
between them.
A single magnetic pole has never been isolated (i.e. magnetic poles are always
found in pairs).
All attempts to date to detect an isolated magnetic pole have been unsuccessful
– although there is some theoretical basis for the existence of monopoles –
single poles.
No matter how often you cut a permanent magnet in two, each piece will always
have a north and a south pole.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Fields
Remember – an electric field surrounds any electric charge.
Similarly, a magnetic field surrounds any permanent magnet.
In addition, the region of space surrounding any moving electric charge also
contains a magnetic field.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Fields
The magnetic field is a vector quantity, and is symbolised by B
The direction of B is given by that which the north pole of a compass needle
points.
Magnetic field lines trace this direction in space, and can be used to visualise the
magnetic field.
Just as electric field lines can be drawn to visualise the electric field!
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Fields around a Bar Magnet
If we were to take a compass and move it
around a bar magnet, the compass arrow
would turn in such a way that we could use
it to trace out the magnetic field lines.
Electric field lines ran from positive charges
to negative charges.
Magnetic field lines point from the magnet’s
North pole to its South pole.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Fields around a Bar Magnet
Iron filings can be used to show the pattern of the
magnetic field lines.
Remember – the direction of the field is the direction
that a north pole would point.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Fields for Opposite Poles
Again, iron filings can be used to show the pattern of the
magnetic field lines.
Compare to the electric field produced by an electric
dipole, as shown below:
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Fields for Like Poles
Iron filings yet again…
Compare to the electric field produced by two like
charges, as shown below:
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Earth’s Magnetic Poles
More proper terminology would be that a magnet has “north-seeking” and
“south-seeking” poles.
The north-seeking pole points towards the north geographic pole (which
corresponds to the Earth’s south magnetic pole).
The south-seeking pole points towards the south geographic pole (which
corresponds to the Earth’s north magnetic pole).
The configuration of the Earth’s magnetic field is very much like that which
would be achieved by burying a gigantic bar magnet deep in the Earth’s interior.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Earth’s Magnetic Poles
The source of the Earth’s magnetic field is thought to be convection currents in
the Earth’s core.
The magnetic field may well be the result of plate tectonics!
Of the four terrestrial planets, Mercury,
Venus, Earth and Mars, only the Earth
has a strong magnetic field.
The giant planets (Jupiter, Saturn, Uranus
and Neptune) have much stronger fields
than the Earth.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Earth’s Magnetic Poles
It is well established that the direction of Earth’s magnetic field reverses
periodically, on timescales of hundreds of thousands of years to a few million
years (with the reversals typically thought to take between 1,000 and 10,000
years).
Earth’s magnetic field
protects Earth’s atmosphere
and is the reason Aurorae
are visible most frequently
near the Earth’s magnetic
poles.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Field and Sunspots – a slight aside
The Sun, on Sunday evening… (18th August, from http://spaceweather.com )
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Field and Sunspots – a slight aside
The Sun, in 2001…
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Field and Sunspots – a slight aside
Sunspots and the magnetic field of the Sun
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Field and Sunspots – a slight aside
Coronal Loops in the Sun’s atmosphere – material follows the magnetic field
lines.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Magnetic Fields and Forces
The magnetic field, B, at some point in space can be defined in terms of the
magnetic force, FB.
Note: B is sometimes known as the Magnetic Induction
A magnetic force will be exerted on a charged particle moving in a magnetic field
(with a velocity v).
Assume, for now, that there are no gravitational or electric fields present…
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
FB on a Charge Moving in a Magnetic Field
The magnitude, FB , of the magnetic force exerted on the particle is proportional
to both the charge, q, and the speed, v, of the particle.
The direction of the force depends on the velocity of the particle and the
direction of the magnetic field. The direction of the force is perpendicular to
both the particle’s velocity, and the direction of the magnetic field.
If the particles velocity vector makes any angle θ ≠ 0 with the field, the force
therefore acts in a direction perpendicular to the plane formed by the velocity
and the field.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
FB on a Charge Moving in a Magnetic Field
The magnetic force exerted on a positive charge is in the direction opposite the
direction of the magnetic force exerted on a negative charge moving in the same
direction.
The magnitude of the magnetic force is proportional to the sine of the angle (θ)
that the particle’s velocity makes with the direction of the magnetic field.
i.e.
𝐹𝐵 ∝ sin 𝜃
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
FB on a Charge Moving in a Magnetic Field
Mathematically, the magnetic force is expressed as:
𝑭𝑩 = 𝑞𝒗 × 𝑩
where:
FB
is the magnetic force
q
is the charge
v
is the velocity of the moving charge
B
is the magnetic field
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Direction
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Direction: The Right-Hand Rule
The rule is based on the right-hand rule for the
cross product.
Your thumb points in the direction of the force,
if q is positive.
The force is in the opposite direction to your
thumb, if q is negative.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
The Magnitude of FB.
The magnitude of the magnetic force on a charged particle is:
𝐹𝐵 = 𝑞 𝑣 𝐵 sin 𝜃
Where θ is the angle between v and B
FB is zero when v and B are parallel or antiparallel (i.e. if θ = 0⁰ or 180⁰).
FB is a maximum when v and B are perpendicular (i.e. when θ = 90⁰)
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
An Example.
A proton moves at a velocity v = 8 x 106 ms-1 in the x-direction.
It enters a region with a magnetic field of B = 2.5 T directed at 60⁰ to the x-axis in
the x-y-plane.
What is the initial force on the proton?
From the right hand rule, we know that the force acts in the z-direction.
𝐹 = 𝑞𝑣𝐵 sin 𝜃
∴ 𝐹 = 1.6 × 10−19 C . 8 × 106 ms −1 . 2.5 T . sin 60°
∴ 𝐹 = 2.77 × 10−12 N
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Differences Between Electric and Magnetic Fields
1) Direction of force
The electric force acts along the direction of the electric field.
The magnetic force acts perpendicular to the magnetic field.
2) Motion
The electric force acts on a charged particle regardless of whether it
is moving.
The magnetic force acts on a charged particle only when the particle
is in motion.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Differences Between Electric and Magnetic Fields
3)
Work
The electric force does work in displacing a charged particle
The magnetic force associated with a steady magnetic field does no
work when a particle is displaced (since the force is perpendicular to
the displacement at its points of application, and so F.ds = 0)
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Work in Magnetic Fields
The kinetic energy of a charged particle moving through a magnetic field cannot
be altered by the magnetic field alone.
When a charged particle moves with a given velocity through a magnetic field,
the field can alter the direction of the velocity, but not the speed of the particle.
The kinetic energy of the particle is therefore not changed by the magnetic
field.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Units of Magnetic Field
The SI unit of magnetic field is the tesla (T).
Since we know that
𝐹𝐵 = 𝑞 𝑣 𝐵 sin 𝜃
N
N
1T=1 m=1
Am
C
s
Where A is the amp, which is the SI unit of electric current, which is Cs-1
You will sometimes here of magnetic fields measured in gauss (G) – this is the
cgs unit of magnetic field, and
1 T = 104 G
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
A quick note on notation…
When we want to represent magnetic field lines on a figure,
there will be many occasions when those lines will either go
into the page, or come out of it.
The convention we use is that dots represent arrows that are
coming out of the page, and crosses represent arrows going
into the page.
This is a standard notation, and can be used when plotting
other vector quantities.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Typical Magnetic Field Values
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Quick Quiz
The north-pole end of a bar magnet is held near a positively charged piece of
plastic. The plastic is:
a) Attracted
b) Repelled
c) Unaffected by the magnet
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Quick Answer
The north-pole end of a bar magnet is held near a positively charged piece of
plastic. The plastic is:
c) Unaffected by the magnet
The magnetic force exerted by a magnetic field on a charge is proportional to
the charge’s velocity relative to the field.
If the charge is stationary, as in this situation, then there is no magnetic force.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Quick Quiz
A charged particle moves with velocity v in a magnetic field B.
The magnetic force on the particle is a maximum when v is:
a) Parallel to B
b) Perpendicular to B
c) Zero
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Quick Answer
A charged particle moves with velocity v in a magnetic field B.
The magnetic force on the particle is a maximum when v is:
b) Perpendicular to B
The maximum value of sin θ occurs when θ = 90⁰.
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Quick Quiz
An electron moves in the plane of the screen towards the top of the screen.
A magnetic field is also in the plane of the screen, directed to the right.
The direction of the magnetic force on the electron is therefore:
a) Toward the top of the screen
b) Toward the bottom of the screen
c) Toward the left edge of the screen
d) Toward the right edge of the screen
e) Out of the screen
f)
Into the screen
Electricity & Magnetism – Magnetism
20/08/2013
PHYSICS 1B – Magnetism
Quick Answer
An electron moves in the plane of the screen towards the top of the screen.
A magnetic field is also in the plane of the screen, directed to the right.
The direction of the magnetic force on the electron is therefore:
e) Out of the screen
The right hand rule gives the direction.
Be sure to account for the negative charge on the electron!
Electricity & Magnetism – Magnetism
20/08/2013