Chapter 30 Faraday’s Law
Michael Faraday was a self-taught physicist who developed his ideas in the early 1800’s. His work with electricity and magnetism led him to realize that while a current creates a magnetic field, a magnetic field can be used to create a current. Faraday’s Law describes another form of the connection between magnetism and electricity. We encountered the first connection when we studied Ampere’s Law. The fact that magnetism can be used to create a current makes it possible to generate electricity at power plants. The consequences of this law are partly responsible for the high mile/gallon characteristic of hybrid cars. If this law was not true transformers for our electrical power distribution system would not work. A multitude of other applications involving electricity would not work if Faraday’s Law was not true.
page 2 Electric Field of Static Charges For the case of static charges the sum of the dot product of the electric field and an element of path around a closed path is zero. This is not the interesting case that leads to useful applications.
Why is the sum of E dot dl equal to zero around the closed path for the case of static charges?
page 3 Magnetic Force Experiment
Use your right hand to verify that the force on the electrons in the wire in
Figure 3b is down the page, as shown, when the loop is moving as shown with
a magnetic field as shown. Which side of the gap on the right side of the
wire has the higher electric potential?
In experiments it is observed that the potential difference across the gap
is larger if the velocity of the wire is larger. Why might this be the
case?
In experiments it is observed that the potential difference across the gap
is zero if the velocity of the wire is zero. Why might this be the case?
Other than the velocity, what could be changed in this experiment in order
to produce a larger potential difference across the gap?
You can skip equation 5.
page 5 Air Cart Speed Detector
How could you apply the concepts discussed in the previous section to build
a velocity detector?
pages 6,7,8 You can skip these pages.
page 9 A Relativity Experiment
PHY162 may discuss this section
page 11 Faraday’s Law
The preceding pages described that an electric potential exists across the
gap in a wire when the wire is moving in the presence of a magnetic field.
An electric potential can also be observed across the gap if the wire
remains stationary and the strength of the magnetic field changes.
Magnetic Flux
Magnetic flux is calculated in the same way as we calculated electric flux.
The flux value is equal to the dot product of the magnetic vector and the
area vector. Given that a uniform magnetic field exists and there is a
certain area for the field to pass through, what conditions lead to the
maximum value for the flux? You may wish to write the equation for the flux
that replaces the dot product with its computational equivalent.
Flux = B A cos(theta)
*List three ways in which the value of the flux can be changed.
page 12 One Form of Faraday’s Law
equation 11: dx is a infinitely small distance dt is an infinitely
small amount of time
Figure 11 Why does the flux through the wire coil decrease?
Equation 15 The electric potential is equal to the negative of the rate of
change of the magnetic flux.
Equation 15a In a situation with more than one loop of wire, each loop has
an area and a corresponding magnetic flux. The electric potential for a
multiloop coil is found by multiplying the negative of the rate of change of
flux by N, where N is the number of turns of wire in the coil.
Suppose that a voltage of 0.02 volts is measured in Figure 11. Now a coil
with 20 turns of wire with the same length and width as the loop in Figure
11 replaces the loop. Predict the value of the observed voltage.
page 13 A Circular Electric Field
Figure 12 The source of the magnetic field has been turned off. The
magnetic field is getting weaker. While the magnetic field is getting
weaker it is observed that a potential difference exists across the gap in
the wire loop. The potential difference exists because an Electric field
exists in the wire. This electric field forces electrons to move in the
wire. The electric field is circular, not because the wire is bent into a
circular shape, but because that is the shape of the electric field
generated when the magnetic field strength changes.
page 14 Recall from Chapter 26 (equation 14) that V = E d . The potential
difference is equal to the value of the (constant) Electric field multiplied
by the displacement. This is another dot product situation and we will
assume that the electric vector and the displacement are parallel. For the
case of a circular path the length of the displacement is the circumference.
At every point along the path the electric field is parallel to the
displacement.
Line Integral of E around a Closed Path
The line integral is a sum completely around a closed path of the dot
product of the electric field and infinitesimally short displacements. This
is the same mathematical calculation that we used in evaluating Ampere’s
Law. You can observe that the right side of Ampere’s Law is different from
the right side of Faraday’s Law. This difference will be reduced in a
future chapter.
Using Faraday’s Law
What questions do you have on this section?
Right Hand Rule for Faraday’s Law
What questions do you have on this section?
page 16 Electric Field of Static Charges
There is no generated electric field for the case of static charges.
When the magnetic flux is changing then an electric field is produced. This
electric field will create a force on a charged particle.
pages 16 - 18 The Betatron
Briefly describe how the charged particles are accelerated in a Betatron.
pages 18-20 Two Kinds of Electric Field We will skip this section
page 21 Applications of Faraday’s Law
Hopefully you now understand the basic concepts that relate to Faraday’s
Law. You should come to my office if you are not sure about the concepts we
discussed in class.
The AC Voltage Generator
Why would the magnetic flux value be changing in Figure 19?
page 22 The angle theta between the magnetic field vector and the area
vector can be computed at any time by multiplying the angular velocity
(radians/sec) by the elapsed time in seconds. This is used to create
equation 23. The rate of change of the magnetic flux is given by equation
24. Equation 25 describes the voltage at the ends of the loop of wire as a
function of the angular velocity, the number of turns of wire, the magnetic
field strength, the area of the loop, and the time. What is the value of
the maximum voltage? Use symbols for your answer.
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