Chapter 1: The "Motor effect" - 12-12-2014
by australiancurriculumphysics - Australian Curriculum Physics (ACP) - http://australiancurriculumphysics.com.au
Chapter 1: The "Motor effect"
by australiancurriculumphysics - Friday, December 12, 2014
http://australiancurriculumphysics.com.au/fathoming-physics-hsc-textbook/motors-andgenerators/1-1-introduction-to-electromagnetism/
Overview of Electromagnetism
Electromagnetism is one of the four fundamental forces that exist in our universe.
There are four fundamental equations of electromagnetism, known as `Maxwell’s equations’ which
describe how charges produce electric and magnetic fields.
There are also two `force laws’ which describe how electric and magnetic fields exert forces on charges.
A descriptive summary of Electromagnetism
The following is a short, snappy summary of electromagnetism.
1. Charges produce electric fields & electric fields exert forces on charges
2. Moving charges produce magnetic fields & magnetic fields exert forces on moving charges
3. A changing (time varying) magnetic field produces an electric field & a changing electric field
produces a magnetic field.
Isn’t electromagnetism beautiful in its symmetry?
A more sophisticated qualitative description of Electromagnetism
We can tease the very short summary in the previous section out a little into two parts, firstly, how
electric charges produce electric and magnetic fields, and secondly, how electric and magnetic fields exert
forces on charges.
How electric charges produce electric and magnetic fields
The table below contains a little more detail about the type of electric and magnetic fields that be
generated by electric charges. The four statements in this table are designed to have a one-to-one
correspondence with Maxwell’s four equations of electromagnetism.
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Chapter 1: The "Motor effect" - 12-12-2014
by australiancurriculumphysics - Australian Curriculum Physics (ACP) - http://australiancurriculumphysics.com.au
Qualitative description of
each of Maxwell’s equations.
Just for fun, here are Maxwell’s equations in integral form, along with an engraving of Maxwell himself.
(Left) Engraving of
James Clerk Maxwell by G. J. Stodart, 1890. (Right) Maxwell’s equations.
The forces on a charge due to electric and magnetic fields
We have covered (briefly and qualitatively) how charges produce electric and magnetic fields. In this
section we will deal with how electric and magnetic fields exert forces on charges.
The force on a charge due to an electric field
In the preliminary course you should have been introduced to the equation relating the electric field
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Chapter 1: The "Motor effect" - 12-12-2014
by australiancurriculumphysics - Australian Curriculum Physics (ACP) - http://australiancurriculumphysics.com.au
strength
to the force
on a charge
We will use this equation in the first part of the topic ‘Ideas to Implementation’.
The force on a moving charge in a magnetic field
Experimentally, the force on a charge
found to be:
moving with a velocity
at an angle
to a magnetic field
is
(1)
in a direction given by the “right-hand-rule” shown below. The right hand rule specifies that the force on
a positive charge moving in a magnetic field is in the direction of the palm of your right hand, if your
thumb points in the direction of the velocity of the charge and your fingers in the direction of the
magnetic field. The force on a negative charge is in the opposite direction.
The right hand palm rule.
This means that in a reference frame in which the charge is stationary, there is no magnetic force on the
charge. If the charge is moving, but it is moving along the field lines, so that
or
, then
there is no magnetic force.
We will use this equation in the first part of the topic ‘Ideas to Implementation’.
The force on a current carrying wire in a magnetic field
In the current topic, Motors & Generators, we are interested in applying the fundamental equation for the
force on a charge moving in a magnetic field, equation (1) to determine the force on a length of wire
carrying a current (which consists of moving charges) in a magnetic field.
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Chapter 1: The "Motor effect" - 12-12-2014
by australiancurriculumphysics - Australian Curriculum Physics (ACP) - http://australiancurriculumphysics.com.au
If the charges that are moving through a magnetic field are part of a current in a conductor, then we can
determine the force that acts on the conductor as a whole by adding up the forces on each individual
charge which makes the current. If is the density of free electrons in the conductor, then the number of
current carrying charges in a volume
(where is the area of the segment of wire and its length) is
. Each of these electrons carries
charge
and travels with a drift velocity
. Using equation (1), the total force acting upon the conductor is
therefore
We note that the current through a conductor of cross-sectional area
The force is therefore
is given by
(2)
in a direction that can also be obtained from the right hand rule in figure where in this case the velocity of
the charges is the direction of current flow in the wire, as illustrated below.
The force on a current
carrying wire with length L in a magnetic field that is directed into the page.
top
Cite this chapter as: T.E. Humphrey, “Chapter 1: The “Motor effect”,” in Fathoming Physics (HSC),
December 12, 2014, http://australiancurriculumphysics.com.au/fathoming-physics-hsc-textbook/motors-
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Chapter 1: The "Motor effect" - 12-12-2014
by australiancurriculumphysics - Australian Curriculum Physics (ACP) - http://australiancurriculumphysics.com.au
and-generators/1-1-introduction-to-electromagnetism/.
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