Magnetic fields were first discovered over 2000 years ago and used for navigation starting in 1000 AD. A magnetic field is a region of space where a magnetic force is experienced. Magnetic field lines represent the direction and strength of a magnetic field. Electric currents produce magnetic fields according to the right-hand rule. Charged particles experience a magnetic force when moving through a magnetic field according to another right-hand rule. Magnetic fields have many applications including mass spectrometers and cyclotrons.

1. MAGNETIC FIELDS

2. History
• Magnets were first discovered over 2000 years ago by the
Chinese and the Greeks and were used for various non
scientific purposes.
• The name was coined by the Greeks, as certain magnetic rocks
(magnetite) were found in the province of Magnesia.
• Unlike electrical effects due to the rubbing of various
substances, like amber, to separate the electrical charges so
there would be attractive and repulsive forces, these magnets
came out of the ground already attracting and repelling certain
materials.

3. History
• It wasn't until after the 1000 A.D. that Chinese, European
and Persian mariners separately used magnets for
navigation. When a magnetic material, shaped in the form
of a needle and floated on the surface of water, it always
pointed in the same direction - towards the north.
• Always being able to tell which direction was north was a
critical factor in ushering in the age of exploration.
• It wasn't until 1600 when this phenomenon was explained
by William Gilbert.

5. So each atom is acting as a magnet with a north and south pole.

7. Law of magnets
• The law of magnets implies that around any magnet, there is a region
where a magnetic pole will experience a force. This region is known as a
magnetic field.
• A magnetic field is a region of space where a magnetic pole experiences
a force. It is a region of space where a force will act upon, without
contact, another magnet or current carrying wire or any magnetic
material.
• Magnetic fields are not visible but they may be represented by lines of
magnetic force or magnetic field lines or magnetic flux. A simple way of
imagining magnetic field lines is to think of one such line as the direction
in which a free magnetic north pole would move if placed in the field.

8.  Magnetic field of a bar magnet
The iron filings line up with the magnetic
field of the bar magnetic field of the bar
magnet which is under the sheet of
paper. A plotting compass will give the
direction of the field.
Magnetic Fields:
• A magnetic field is a vector, and the direction of the field at any
point is defined as the direction of the force on a north pole placed
at the point.
• Magnetic field lines may be plotted using a small compass (a
plotting compass) or by the use of iron filings and a compass.

9. Properties of magnetic lines of force
1. Lines of force never intersect or cross, the line are unique at any
point in space.
2. Points out of a North pole and into a south pole.
3. A line (curve) such that tangent to it at any point is the direction
of the field at this point.
4. Magnetic field lines always form closed loops. (They are always
continuous – they do not begin or end as electric field lines do on
charges, since there are no monopoles).
5. The strength of magnetic field is proportional to the closeness of
lines. It is exactly proportional to the number of lines per unit area
perpendicular to the lines.

10. Magnetic Fields
• Arbitrarily, magnetic field lines are defined as leaving the north pole
of the magnet and reentering at the south pole as seen below. The
lines specify the direction that the north pole of a magnet will point
to.
• The more lines per unit
area, the stronger the field.
• The lines that seem not to be
in loops are - we just ran out of
room on the slide. All
magnetic field lines form
complete loops.

11. Magnetic Fields
Like Electric Fields, different configurations of magnets will produce
interesting Magnetic Fields.
Two magnets with their opposite poles
next to each other - these magnets are
attracting each other.
Two magnets with their north poles next
to each other -these magnets are repelling
each other

12. The Earth's Magnetic Field
• The Earth’s magnetic field is similar to that of
a bar magnet.
• It is caused by the circulation of molten iron
alloys in the earth's outer core.
• The Earth’s “North Pole” is really a south
magnetic pole as the north ends of magnets
are attracted to it.
• The magnetic poles are not located along the
• earth’s axis of rotation.

13. Types of magnets
• Permanent magnet – Do not depend on electrical energy to keep its
magnetic properties. Usually made of steel which is difficult to
magnetize but does not lose its magnetism easily.
The ability of a magnet to attract magnetic substances is called
magnetism.
• Electromagnets – are temporary magnets made by passing electric
current through a coil of wire. Usually made of iron which is easily
and strongly magnetized and also easily loses its magnetism.
 Electromagnets are made stronger by wrapping the coil around an
iron core, adding more turns to the coil, by increasing the current
flowing through the coil and moving coil more quickly relative to the
magnet.

14. Units
S.I. Unit of magnetic flux is Weber (Wb)
Unit of magnetic flux density B is Tesla (T) and is defined as the
force per unit length, per unit current (N/m/A)
Repulsion is the sure test for the polarity of a magnet because a
pole repels a like pole but attracts both an unlike pole and an
unmagnetized magnetic material.

15. Electric Currents Produce Magnetic Fields
• It has been experimentally observed that the direction
of the magnetic field depends on the direction of the
electric current.
• The direction of the field is given by the right-hand grip
rule or corkscrew rule. Orient your right hand thumb in
the direction of the current. The B field follows the
path followed by your curled
fingers.

16. Electric Currents Produce Magnetic Fields
• When you have a current circulating around
an iron core, a magnetic field is created and
the device is called an electromagnet.
• This is an industrial electromagnet that
when the current is turned on, it picks up
metallic objects. Metal scrap is being
attracted from the ground to the
electromagnet.

17. Direction of Magnetic Fields
• Another difference between electric fields and magnetic fields, is that
we can normally understand an electric field very easily on two
dimensional paper (the electric field is, of course, three dimensional,
but is easily represented in two dimensions).
• But the magnetic field is looping around the wire so magnetic fields
need to be shown as three dimensional to be understood. Somehow,
we need to show this third dimension on our paper.
We have left / right:
Up / down:
• How do we represent the third dimension on a page of paper?

18. Direction of Magnetic Fields
Picture the field line (which is a vector with magnitude and direction)
like an arrow. The head of the arrow is the direction of the field.
If the magnetic field is into the page, you will see the tail of the arrow:
If the magnetic field is out of the page, you will see the front of the
arrow:

19. Electric Currents Produce Magnetic Fields
• Here's how the magnetic field would look
inside a current carrying loop.
• Your thumb points in the direction of the
current, and your fingers curl around and
show the magnetic field coming out of the
board within the loop.
• What direction is the magnetic field
outside the loop? That’s right - into the
board, as your fingers continue curling.

20. Force on a Charged Particle Moving in a Uniform
Magnetic Field
• Not only do magnetic poles exert a force on each other, but a
magnetic field will exert a force on a moving charge.
• If the charge is not moving - it does not feel the force. This is
a unique concept and phenomenon in the universe.
• The force on a moving charge is related to the magnitude of
its charge, velocity and strength of the magnetic field - but
only the portion of the magnetic field that is perpendicular to
the charge’s motion.
• The force is given by
𝑭 = 𝒒𝒗𝑩𝒑𝒆𝒓𝒑𝒆𝒏𝒅𝒊𝒄𝒖𝒍𝒂𝒓

21. Force on a Charged Particle Moving in a Uniform Magnetic Field
• The direction of the force on a positive
charge is perpendicular to both the direction of the
charge’s velocity and the magnetic field.
• It is found by putting your forefinger (or
all four fingers) in the direction of the
charge’s motion, then curling your fingers
in the direction of the magnetic field. The
thumb will point in the direction of the
magnetic force.
• NOTE: if the velocity of the charge is in the same
direction as the magnetic field - there is no force on
the charge.
This is different from the right-hand grip rule shown earlier, that found the
magnetic field direction due to an electric current.

22. Force on Electric Charge Moving in a Magnetic Field
• Since the magnetic force is perpendicular
to the charge’s velocity, we have a "center
seeking" force, which results in centripetal
motion - the charge moves in a circle.
• An electron injected with velocity, v, into
the magnetic field on the right will have a
magnetic force directed to the right at all
times (towards the middle of a circle). A
positive particle will move in a counter
clockwise path.

23. Force on Electric Charge Moving in a Magnetic Field
Because 𝑭 produces the centripetal acceleration, we can equate its
magnitude, 𝒒𝒗𝑩 in this case, to the mass of the particle multiplied by
the centripetal acceleration 𝒗𝟐/𝒓. From Newton’s second law, we find
that
which gives
This equation says that the radius of the path is proportional to the
momentum m𝒗 of the particle and is inversely proportional to the
charge and the magnetic field. This is called the cyclotron equation
because it’s used in the design of these instruments (popularly known as
atom smashers).

24. Example: Force on a Moving Charge
A positive charge moving with a constant velocity v enters a region of a
uniform magnetic field pointing out the page. What is the direction of the
magnetic force on the charge?
Solution
Using the right hand rule
Step 1: Point the four fingers of your right hand
in the direction of the charge’s velocity (left).
Step 2: Curl your fingers perpendicular to your
palm and point them in the direction of the
magnetic field (out of the page).
Step 3: Extend your thumb perpendicular to your fingers – it is pointing in the
direction of the magnetic force on a moving positive charge (up).

25. Example: A proton (e = 1.6𝑥10−19
), moving at a speed of 3.0 𝑥104
m/s enters a
Magnetic Field of 0.55 T moving out of the page. Find the direction and the
magnitude of the Magnetic Force on the proton.
Given: q = 1.6𝑥10−19 C, v = 3.0 𝑥104 m/s, B = 0.55 T
Magnetic force equation
Step 1: Point the four fingers of your right hand in the direction of the charge's
velocity (down).
Step 2: Curl your fingers perpendicular to your palm and point them in the direction
of the magnetic field (out of the page).
Step 3: Extend your thumb perpendicular to your fingers – it is pointing in the
direction of the magnetic force on a moving positive charge (left).

26. Example: An electron (q = −1.6𝑥10−19
C) has a horizontal velocity of 6.0 𝑥105
m/s
towards the east. It travels through a 0.24 T uniform magnetic field which is directed
straight down. What is the direction and magnitude of the magnetic force on the
electron?
Given: q = −1.6𝑥10−19
C,
v = 6.0 𝑥105
m/s, B = 0.24 T
Step 1: Point the four fingers of your right hand in the direction of the charge's
velocity (east).
Step 2: Curl your fingers perpendicular to your palm and point them in the direction
of the magnetic field (into the page).
Step 3: Extend your thumb perpendicular to your fingers – it is pointing in the
direction of the magnetic force on a moving positive charge (up).
Since the charge is negative, reverse the direction of the force obtained by the right
hand rule. The force is to the south.

27. Magnetic Field Force on a current carrying wire
The force on the wire depends on the current, the length of the wire,
the magnetic field, and its orientation
𝑭 = 𝐈𝑳𝑩𝒑𝒆𝒓𝒑𝒆𝒏𝒅𝒊𝒄𝒖𝒍𝒂𝒓
𝐈 is the current
𝐋 is the length of wire
𝐁 is the magnetic field (perpendicular to both the force and current)

28. Example: A 0.5 m long wire carries a current of 2.0 A in a direction
perpendicular to a 0.3 T magnetic field. What is the magnitude of
the magnetic force acting on the wire?
Solution

29. Applications of Magnetic Forces and Fields
Mass Spectrometer
A Mass Spectrometer is used to separate out atoms and molecules
based on their mass - and is used to analyze the physical makeup of
substances in terms of their relative concentrations of their constituent
parts.
Cyclotron
A cyclotron accelerate charged particles (usually protons, deuterons, or
alpha- accelerate charged particles (usually protons, deuterons, or
alpha- particles) to large kinetic energies. These particles are then used
for nuclear-collision experiments to produce radioactive isotopes.

33. References
• Physics Principles and Applications by Giancoli, 7th
Edition, 2014 Pearson Education, Inc.
• University Physics Volume 1, OpenStax (2018), Rice
University