This Set o’ Slides - Day 19, Wednesday, Feb 17
•
•
•
•
•
•
Chapter 32 Magnet Fields and Forces
Magnetism
Magnetic Fields
Direction of Magnetic Field
Right Hand Rule for Field Direction
Magnetic Field of Moving Charge or Current –
Biot-Savart Law
• Cross Product. Biot-Savart Law as cross product.
• More right hand rules. Three total! Similar but
different!
Day 19, Wednesday, Feb 17, Announcement(s)
• Exam 2 covers Chapters 28-31 (electric potential through
circuits.)
• Lecture material for next three (lecture) days (including
today) is not on the second midterm exam.
• MIDTERM 2 HELP/STUDY SESSION:
Saturday, Feb 20, 2016,
2-5:00 pm,
in Weniger 212.
Magnetic Fields and Forces
• Magnets, like electric charges, exert forces on each other.
• Forces are either attracting or repelling.
• Likes repel (each other); opposites attract.
• But, the “likes” and “opposites” here are poles.
• North and South are the opposite words for poles.
• While single charges exist, single poles – monopoles – have
never (yet?!) been discovered/found/observed.
• Since magnets only come in dipoles, fields can’t really start
and end (as electric fields do on charges.)
• Magnetic fields form continuous loops, with a well-defined
direction, though no (clear) start and end.
•
•
•
•
Magnetic Fields
A magnetic field, akin to the electric field, in a region of
space surrounding some magnet can be thought of as a
“mapping” of the magnetic force which is exerted on other
magnets in that region.
It can be envisioned as the lines representing the direction
of magnetic force in that region (on some small magnet
sitting in that region.)
This force will always be on a magnetic dipole, a small
compass needle for example, causing alignment of the
magnet with the field as well as repulsion or attraction of
the magnet.
Magnets create fields around them and magnets are pushed
or pulled or rotated (forced around) by magnetic fields.
Drawing Field Lines of a Bar Magnet
Slide 24-16
Magnetic Fields Produced by Bar Magnets
Two bar magnets,
unlike poles facing
Two bar magnets,
like poles facing
Slide 24-18
Magnetic Fields
• Magnetic fields are continuous; they don’t start and/or end
at the poles of a magnet but always form closed loops,
which pass through the magnet itself from south to north.
• The direction of the magnetic field (at some point) is
determined by the direction a small compass would point (at
that point.)
• Outside of the magnet, (the convention is that) magnetic
fields always point away from north poles and towards
south poles.
• Inside the magnet, the field points from south to north.
Magnetic Field Lines
• Magnetic field lines, drawn for some magnet, are a construction
that help us envision what the field might look like were it actually
visible.
• The lines (outside the magnet) always point away from north poles
and towards south poles, but they don’t end there, but instead, loop
around through the magnet from south back to north.
• A tangent line at any point shows the direction of the magnetic
field at that point.
• Magnetic field lines never cross in space.
• The density of lines in some region is proportional to the strength
of the field in that region.
• You should be able to recognize and draw simple field line
patterns.
Magnetic Field Lines, Earth Example
• Several interesting things to note about our own Earth’s
field…
• Since the north end of a compass points “north” on Earth,
our Earth’s north (magnetic) pole must actually be a south
pole! (It is.)
• Magnetic north and geographic north (rotational axis point)
are not the same place!
• The angle of declination is the angle between magnetic
north and geographic north.
• Dip angle is angle of the field relative to the surface.
Where Does Magnetism Come From?
• Electrons! But not sitting-still electrons. Electrons in motion
• Any moving charge creates a magnetic field around it.
• This inter-connectedness of charge and magnetic fields
combined the study of the two into one electromagnetic
theory. The two are just about inseparable.
• We’ll look at a examples of calculable magnetic fields due
to currents. Some of which will require calculus.
• For a long, straight wire with a current running through, a
magnetic field is created that encircles the wire.
• Remember, the magnetic fields always form closed loops, in
this case, circles.
Magnetic Field Due to a Long, Current-Carrying Wire
• The magnitude of the magnetic field at a perpendicular
distance r away from the long wire is found via:
B = μ0 I / (2 π r)
B = magnetic field strength. SI units will be the tesla (T).
μ0 = permeability of free space constant = 4π x10-7 T m/A
= 1.257x10-6 T m/A
I = current in amperes
r = radial distance from the wire to the point where the field
strength is computed (in meters).
The direction of the field is the direction as determined from a
right hand rule.
Magnetic Field is a Vector Quantity
• On previous slide, it mentioned direction of magnetic field.
• Magnetic field is a vector quantity.
• Summing up magnetic fields from multiple sources means a
vector sum.
• A magnetic force, like every stinkin’ force, is also a vector
quantity. Direction, direction, direction…
• From where comes the direction? Right hand rules!
Magnetic Field – Teslas
• 1 tesla (1 T) is a large magnetic field. (MRI size.)
• The Earth’s field is (approximately) 25-50 μT.
• 1 tesla = 1 N s / (C m) = 1 N / (A m) = 10,000 gauss
Right Hand Rule (first one anyway)
• The direction of the magnetic field surrounding a currentcarrying wire can be found by a right-hand rule.
– Stick out your thumb so that it points in the direction of the
moving current (or any single moving, positive charge.)
– Curl your fingers (as if gripping the wire) and your fingers will
wrap around the wire as the field wraps around wire, your
fingertips pointing in the direction of the field.
– Notice, “away from north pole, towards south pole” no longer
make much/any sense here!
Slide 24-24
X’s and Dot’s
• Drawing currents and fields in multiple dimensions isn’t an
easy task sometimes.
• Because of the interaction between magnetic fields and
moving charges, we’re going to have to think in 3-D.
• Instead of forced-perspective 3-D drawings, we’ll draw our
vectors in the plane of the paper as usual.
• We’ll represent the current or vectors going into or out of
the plane (paper) with either an “X” for into the paper (think
back side of an arrow where you’re looking at the feathers)
or a “Dot” for coming out of the paper (think point of
arrowhead coming towards you.)
Examples
• A long wire that carries 3.0 A current is parallel to a long
wire carrying 5.0 A current. If the wires are separated by 4.0
cm, where along a (perpendicular) line joining the two wires
(the x-axis for example) is the magnetic field zero if the
currents are
a) in the same direction? b) in opposite directions?
• Loop plus wire. What is the B field magnitude and direction
at point P?