1. Ch. 20: Magnetic Fields & Forces
Chapter 27 opener. Magnets produce magnetic fields, but so do electric currents. An electric current flowing in this straight wire produces a magnetic field which causes the tiny pieces of iron (iron “filings”) to align in the field. We shall see in this Chapter how magnetic field is defined, and that the magnetic field direction is along the iron filings. The magnetic field lines due to the electric current in this long wire are in the shape of circles around the wire. We also discuss how magnetic fields exert forces on electric currents and on charged particles, as well as useful applications of the interaction between magnetic fields and electric currents and moving electric charges.

2. Electric Currents Produce B Fields!!
Magnetism Outline
Magnets & Magnetic Fields  B Fields
Electric Currents Produce B Fields!!
Force on Electric Current in a B Field;
Definition of B
Force on a moving Electric Charge
in a B Field
Torque on a Current Loop
Magnetic Dipole Moment  μ

3. Applications: Outline Motors, Loudspeakers, Galvanometers
Discovery & Properties of the
Electron
The Hall Effect
Mass Spectrometer

4. Brief History of Magnetism
13th Century BC: The Chinese
used a compass.
Uses a magnetic needle
Probably an invention of Arabic or
Indian origin
800 BC: The Greeks
Discovered that magnetite
(Fe3O4) attracts pieces of iron

5. He called the points poles
History
1269: Pierre de Maricourt
Found that the direction of a needle
near a spherical natural magnet
formed lines that encircled the sphere.
The lines also passed through 2
points diametrically opposed to
each other.
He called the points poles

6. 1750: Experimenters showed that magnetic poles exert attractive or
1600: William Gilbert
Expanded experiments with magnetism
to a variety of Materials
Suggested the Earth itself was a large
permanent magnet
1750: Experimenters showed that
magnetic poles exert attractive or
repulsive forces on each other.
1819: Found that an electric current
deflected a compass needle

7. James Clerk Maxwell: 1819: Found that an electric current
deflected a compass needle
1820’s: Faraday and Henry
Found further connections between
electricity and magnetism
A changing magnetic field creates an
electric field.
James Clerk Maxwell:
A changing electric field produces a
magnetic field.

8. Hans Christian Oersted
1777 – 1851:
Discovered a relationship
between electricity &
magnetism.
He found that an electric current in a wire will
deflect a compass needle.
He was the first to find evidence of a
connection between electric & magnetic phenomena.
Also was the first to prepare pure Aluminum.

9. Experiments show that: Magnetic fields are produced
Magnetism
Physics is an Experimental Science!
Experiments show that:
Magnetic fields are produced
by moving electric charges
Magnetic fields exert forces on other moving charges

10. The Focus of this chapter:
Magnetism
The Focus of this chapter:
Understand the sources of magnetic fields & the fields they produce
Calculate the magnetic force on a charged particle
Magnetism & electricity are connected
More connections will be studied in later chapters

11. Magnets Permanent magnet applications:
The first observations of magnetic fields involved permanent magnets
Many ancient cultures discovered natural magnetic properties of materials: Magnetite & Others
Permanent magnet applications:
Compass needles
Speakers
Computer hard disks

12. Bar Magnet A bar magnet is a permanent magnet in the shape of a bar.
The symbol for the magnetic field is B.
The magnetic field lines can be found from the pattern of the iron filings
The filings are small, needle-shaped, permanent magnets

13. Magnets & Magnetic Fields
Every magnet, regardless
of its shape, has two ends
called “Poles”. They are the
“North (N) Pole”
& the
“South (S) Pole”
The poles exert forces on one another:
Like poles repel &
opposite poles attract
Figure Like poles of a magnet repel; unlike poles attract. Red arrows indicate force direction.

14. The North pole of a magnet
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 North pole of a magnet
points toward the Earth’s North magnetic pole.

15. Earth’s North magnetic pole is actually a magnetic South pole!
This means that
Earth’s North magnetic pole
is actually a magnetic
South pole!
Similarly,
the Earth’s South magnetic Pole is actually a magnetic
North pole!

16. A single magnetic pole has never been isolated.
The force between two poles varies as the
inverse square of the distance between them.
(Similar to the force between 2 point charges)
A single magnetic pole has
never been isolated.
That is, magnetic poles are always found in pairs.
All attempts so far to detect an isolated magnetic
pole (a magnetic monopole) have been unsuccessful.
No matter how many times a permanent magnet is
cut in 2, each piece always has north & south poles.

17. If a magnet is cut in half, the result isn’t a north pole & a south pole!! The result is two smaller magnets!!
Figure If you split a magnet, you won’t get isolated north and south poles; instead, two new magnets are produced, each with a north and a south pole.

18. Magnetic Fields: Observations
Reminder:
An electric field surrounds
any electric charge.
Similarly,
The region of space surrounding any moving electric charge
also contains a magnetic field.

19. Magnetic Fields: Observations
A magnetic field also surrounds a magnetic
substance making up a permanent magnet.
A magnetic field is a vector quantity. It is
symbolized by B.
The direction of field B is given by the
direction the North pole of a compass needle
points in that location.
Iron filings can be used to show
how the field lines, as traced out by a
compass, would look.

20. Magnetic Field Lines, which are always closed loops.
Magnetic fields can be visualized using
Magnetic Field Lines,
which are always closed loops.
Figure (a) Visualizing magnetic field lines around a bar magnet, using iron filings and compass needles. The red end of the bar magnet is its north pole. The N pole of a nearby compass needle points away from the north pole of the magnet. (b) Magnetic field lines for a bar magnet.

21. Magnetic Field Lines, Bar Magnet
A compass can be used to
trace the field lines.
The lines outside the magnet
point from the North pole to
the South pole.
Iron filings can also be used to
show the pattern of the
magnetic field lines.
The direction of the magnetic
field is the direction a north
pole would point.

22. Magnetic Field Lines
Opposite
Poles
Like
Poles

23. Magnetic Field Lines
The magnetic poles are indicated at the ends of the bar magnet
Called north and south
The magnetic poles are analogous to positive and negative charges
The north poles of the filings are attracted to the south pole of the bar magnet

24. Plotting Field Lines Field lines are three-dimensional
A large dot (•) indicates the tip of the vector when it points out of the plane
A cross (×) denotes the tails of the vector when it points into the plane

25. The SI unit of magnetic field B
Magnetic Fields
The iron filings align parallel to the magnetic field lines
The SI unit of magnetic field B
is the Tesla (T)
The magnetic field lines go from the north pole toward the south pole
The magnitude of the field decreases as you move farther from a pole
The magnetic field lines form closed loops
General property of magnetic fields, not just bar magnets

26. Horseshoe Magnet The field is largest in the horseshoe gap
Can be made by bending a bar magnet
There are poles at the ends of the horseshoe
The field is largest in the horseshoe gap
The field is directed across the gap

27. Earth’s Magnetic Field
Earth’s magnetic field is
very small: BEarth  50 μT
It depends on location &
altitude. It is also slowly
changing with time!
Note!!! The Earth’s magnetic
“North Pole” is really a
South Magnetic Pole,
because the North poles of
magnets are attracted to it.
Figure The Earth acts like a huge magnet; but its magnetic poles are not at the geographic poles, which are on the Earth’s rotation axis.

28. Earth’s Magnetic Field
The source of the Earth’s magnetic field is likely
convection currents in the Earth’s core.
There is strong evidence that the magnitude of a
planet’s magnetic field is related to its rate of rotation.
The direction of the Earth’s magnetic field reverses
Periodically (over thousands of years!).

29. A Uniform Magnetic Field is constant in magnitude & direction.
The magnetic field B between these two wide poles is nearly uniform.
Figure Magnetic field between two wide poles of a magnet is nearly uniform, except near the edges.

30. Electric Currents Produce Magnetic Fields
Experiments show that
Electric Currents Produce Magnetic Fields.
The direction of the field is given by a
Right-Hand Rule.
Figure (a) Deflection of compass needles near a current-carrying wire, showing the presence and direction of the magnetic field. (b) Magnetic field lines around an electric current in a straight wire. (c) Right-hand rule for remembering the direction of the magnetic field: when the thumb points in the direction of the conventional current, the fingers wrapped around the wire point in the direction of the magnetic field. See also the Chapter-Opening photo.

31. Right-Hand Rule. Magnetic Field Due to a Current Loop
The direction is given by a
Right-Hand Rule.
Figure Magnetic field lines due to a circular loop of wire.
Figure Right-hand rule for determining the direction of the magnetic field relative to the current.

32. Force on a Current in a Magnetic Field & the DEFINITION of B
A magnet exerts a force F
on a current-carrying
wire. The direction
of F is given by a
Right-Hand Rule
Figure (a) Force on a current-carrying wire placed in a magnetic field B; (b) same, but current reversed; (c) right-hand rule for setup in (b).

33. This equation defines the Magnetic Field B.
The force F on the wire depends on the current,
the length l of the wire, the magnetic field B & its
orientation:
This equation defines the Magnetic Field B.
In vector notation the force is given by
The SI Unit of the Magnetic Field B is
The Tesla (T): 1 T  1 N/A·m
Another unit that is sometimes used (from the cgs system) is
The Gauss (G): 1 G = 10-4 T

34. Example: Magnetic Force on a
Current Carrying Wire
A wire carrying a current
I = 30 A has length
l = 12 cm between the
pole faces of a magnet at
angle θ = 60° as shown.
The magnetic field is
approximately uniform
& is B = 0.90 T.
Calculate the magnitude of
the force F on the wire.
Solution: F = IlBsin θ = 2.8 N.

35. Example: Magnetic Force on a
Current Carrying Wire
A wire carrying a current
I = 30 A has length
l = 12 cm between the
pole faces of a magnet at
angle θ = 60° as shown.
The magnetic field is
approximately uniform
& is B = 0.90 T.
Calculate the magnitude of
the force F on the wire.
Solution: F = IlBsin θ = 2.8 N.
Solution: Use
Solve & get:
F = 2.8 N

36. Example: Measuring a Magnetic Field
A rectangular wire loop hangs
vertically.
A magnetic field B is directed
horizontally, perpendicular to
the wire, & points out of the
page. B is uniform along the horizontal
portion of wire (l = 10.0 cm) which is
near the center of the gap of the magnet
producing B.
Solution: The wire is perpendicular to the field (the vertical wires feel no force), so B = F/Il = 1.42 T.

37. Example: Measuring a Magnetic Field
The top portion of the loop is
free of the field. The loop
hangs from a balance which
Measures a downward
magnetic force (in addition to
gravity) of
F = 3.48  10-2 N
when the wire carries a current I = A.
Calculate B.
Solution: The wire is perpendicular to the field (the vertical wires feel no force), so B = F/Il = 1.42 T.

38. Example: Measuring a Magnetic Field
The downward magnetic force (in
addition to gravity) is
F = 3.48  10-2 N
when the wire carries a current
I = A.
Calculate B.
Solution:
Use
Solution: The wire is perpendicular to the field (the vertical wires feel no force), so B = F/Il = 1.42 T.
Solve & get: B = 1.42 T

39. Example: Magnetic Force on a Semicircular Wire.
A rigid wire carrying a current
I consists of a semicircle of
radius R & two straight
portions. It lies in a plane
perpendicular to a uniform
magnetic field B0. (Note the
choice of x & y axes).
Solution: The forces on the straight sections are equal and opposite, and cancel. The force dF on a segment dl of the wire is IB0R dφ and is perpendicular to the plane of the diagram. Therefore, F = ∫dF = IB0R∫sin φ dφ = 2IB0R.
The straight portions have length l within the field.
Calculate the net force F on the wire due to B0.

40. Example: Magnetic Force on a Semicircular Wire.
Calculate the net
force F on the wire
due to B0.
Solution gives:
F = 2IB0R
Solution: The forces on the straight sections are equal and opposite, and cancel. The force dF on a segment dl of the wire is IB0R dφ and is perpendicular to the plane of the diagram. Therefore, F = ∫dF = IB0R∫sin φ dφ = 2IB0R.