Download Lecture 5: Pre-reading Magnetic Fields and Forces

Physics E-1bx: Pre-reading for Lecture 5
March 10, 2015
Lecture 5: Pre-reading
Magnetic Fields and Forces
In this lecture we’ll introduce magnetic fields. You certainly know that magnets have
“North” and “South” poles, which get their names because the “North” pole of a magnet will
point (roughly) towards the Earth’s north pole. You also know like poles repel (N–N and S–S),
and unlike poles attract (N–S). So perhaps N and S poles could be a little bit like (+) and (–)
charges, right? Well, almost. The analogies are pretty good, if you think about N as being like
(+) and S as being like (–):
• Magnetic field lines point away from N poles and towards S poles:
Electric field lines point away from (+) charges and towards (–) charges
• The force on a N pole is in the same direction as the magnetic field:
The force on a (+) charge is in the same direction as the electric field
• The force on a S pole is in the opposite direction of the magnetic field:
The force on a (–) charge is in the opposite direction of the electric field
The magnetic field is a vector field, just like the electric field. The magnetic field is given the

symbol B . However, there are some subtle differences
between electricity and magnetism. Most importantly, it
turns out that magnetic field lines never end! They just go
in closed loops. So the magnetic field doesn’t start on N
poles and end on S poles; instead, the field just “bunches
together” at the poles, like in the figure at right. The field
actually continues inside the magnet, making complete
loops. One consequence of this is that you can never
isolate a single magnetic pole—they always come in
N/S pairs. If you try to isolate a pole by breaking a
magnet in half, you just get new poles, and so on.
Fundamentally, the simplest “unit” of magnetism is a
dipole—analogous to the +/– electric dipoles we saw
earlier. There are no monopoles in magnetism.
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March 10, 2015
Since bar magnets act like dipoles, we expect that a bar magnet will feel a torque in an
external applied magnetic field. Indeed that is exactly how a magnetic compass works! The
compass needle feels a torque that will cause it to align with the Earth’s magnetic field—and so
the (magnetic) north pole of the compass will point towards the Earth’s north pole.
In addition to creating magnetic fields from a bar
magnet, you can create a magnetic field from a current. If
there is a current flowing through a long straight wire, the
current will create a magnetic field that “loops” around the
wire, as shown in the figure at right. The magnitude of the
field decreases with distance from the wire, according to the
equation:
µ0 I
2π r
where µ0 is a constant that converts the units (the SI unit of magnetic field is the Tesla).
B=
If the current forms a loop, instead of being in a straight wire, then the loop of current
will create a magnetic dipole field that will look a lot like the field of a small bar magnet. Thus,
a small loop of current creates a “north pole” and a “south pole”—and we’ll see in class exactly
how this works. Remember, magnetic dipoles are a lot like electric dipoles.
Magnetic fields also exert forces on charges, but only if the charge is moving! If a

charge q is moving with a velocity vector v , it turns out that the force on the charge will always
be perpendicular to the velocity of the charge. As you may recall from last semester, a force that
is perpendicular to the velocity will cause the charge to change direction, but won’t make it
speed up or slow down. We’ll need to introduce a new way of multiplying vectors—the cross
product—in order to explain how this all works.
Finally, if you have a wire carrying a current, then that wire has charges in motion! As
you might expect, a magnetic field will exert a force on a current-carrying wire. We’ll see in
class that you can determine this force by adding up the force on all the charges moving in the
wire.
To summarize: magnetic fields are created by permanent magnets and by currents.
Magnetic fields exert forces on permanent magnets, on moving charges, and on current-carrying
wires.
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March 10, 2015
Our last topic for this lecture is electromagnetic induction, which was discovered by
Faraday. Faraday found that if you change the flux of the magnetic field through a loop of wire,
it will induce a current in the wire. Now what is flux? Imagine the magnetic field lines flowing
through space. If you put a loop of wire somewhere, then some of the field lines will flow
through the loop. The amount of field that flows through the loop is called the flux (you can
think of it as a fancy word for “flow”). As we’ll see in class, the flux depends on three things:
• the strength of the field (bigger field = bigger flux)
• the size (or area) of the loop (bigger area = bigger flux)
• the angle of the field with respect to the loop (field is perpendicular gives biggest flux)
Anyway, so Faraday discovered that if you have a loop of wire, and you change the magnetic
flux through that wire, a current will flow through the loop. This is called an induced EMF, or
induced “electromotive force.” As you recall, and EMF is kinda like a voltage—but in this case
it’s a voltage change around a closed loop! That actually violates Kirchhoff’s Laws, but those
laws don’t apply if there are fields that change with time. So with Faraday you get a current
flowing through a loop without any kind of battery. That’s exactly how electric generators work:
everything from a small gasoline-powered backup generator to huge hydroelectric power plants
work because of electromagnetic induction.
•
Learning objectives: After this lecture, you will be able to…
1.
Identify the poles of a magnet, and sketch the magnetic field lines created by a permanent
magnet (like a bar magnet).
2.
Construct an analogy between magnetic poles and electric charges, and explain the
limitations of that analogy.
3.
Construct an analogy between magnetic field lines and electric field lines, and explain the
limitations of that analogy.
4.
Predict the most stable configuration of a magnetic dipole in uniform magnetic field, and
explain why two magnetic dipoles (bar magnets) attract or repel one another.
5.
Calculate and draw the magnetic field created by a current in a long straight wire, using
the right-hand rule to predict the correct direction of the field.
6.
Calculate the magnitude and direction of the magnetic force on a moving electric charge,
using the cross product and the right-hand rule.
7.
Calculate the magnitude and direction of the magnetic force on a long straight wire
carrying an electric current.
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March 10, 2015
8.
Predict the direction of the magnetic force between two long straight wires, both with
currents flowing in them.
9.
Identify the magnitude and direction of the magnetic dipole moment created by a circular
loop of current.
10.
Calculate the energy of a magnetic dipole placed in an external magnetic field.
11.
Define the magnetic flux through a loop of wire, and calculate the flux for a given
magnetic field and loop (including the sign of the flux).
12.
Describe what you can do to change the magnetic flux through a loop, and decide
whether the magnitude of the flux gets larger or smaller for each type of change.
13.
Explain Faraday’s Law of Induction and how it relates changes in magnetic flux with
induced current in a loop.
14.
Use Lenz’s Law to determine the direction of the induced current in a loop.
15.
Calculate the magnitude and direction of the induced current in a loop of wire, given the
change in the magnetic flux and the resistance of the wire, using both Faraday’s Law and
Lenz’s Law.
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