1. Chapter 29: Magnetic Fields
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!!
Chapter 29 Outline
Magnets & Magnetic Fields  B Fields
Electric Currents Produce B Fields!!
Force on an Electric Current in a B Field;
Definition of B
Force on an Electric Charge moving in a B Field
Torque on a Current Loop
Magnetic Dipole Moment  μ
Applications: Motors, Loudspeakers, Galvanometers
Discovery & Properties of the Electron
The Hall Effect
Mass Spectrometer

3. 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
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 two points
Diametrically opposed to each other.
He called the points poles

4. James Clerk Maxwell 1600: William Gilbert 1750: 1819:
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
1820’s: Faraday and Henry
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.

5. 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.

6. 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.

7. 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.
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!

8. A single magnetic pole has In other words, magnetic poles are
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.
In other words, 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.

9. 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.

10. Magnetic Fields
Reminder: An electric field surrounds any
electric charge. Similarly,
The region of space surrounding any moving electric charge
also contains a magnetic field.
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.
Magnetic field lines can be used to show how the field
lines, as traced out by a compass, would look.

11. 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.

12. 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.

13. Magnetic Field Lines
Opposite
Poles
Like
Poles

14. 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.

15. 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!).

16. 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.

17. 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.

18. 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.

19. 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).

20. 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

21. 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.

22. 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

23. 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.
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)
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.

24. Example: Measuring a Magnetic Field
The loop hangs from a balance which
measures a downward magnetic force
(in addition to gravity)
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

25. 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). Straight portions each have length l within the field.
Calculate the net force F on the wire due to B0.
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.

26. 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). Straight portions each have length l within the field.
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.