Reading Guide
for April 15

Chapter 25: Electromagnetic Induction

pp. 477–478. Electromagnetic Induction.  This first section of the chapter jumps right to the heart of the matter: moving a magnet relative to a conductor induces a current in the conductor.  Some other ideas you should pick up in this brief but meaty section:

• How is the number of loops through which a magnet moves related to the induced potential in the loops?
• Given the answer to the previous question, why isn’t it a simple matter to generate more potential by simply increasing the number of loops through which the magnet moves?

pp. 478–479. Faraday’s Law.  The law is given here in words rather than as an equation, because to write the equation requires first defining magnetic field and magnetic flux.  Note that induced potential depends on two factors:

• the number of loops in the wire, and
• the rate of change of magnetic field within the loops.

How much current is produced depends, of course, on the resistance of the wire and the resistance of the circuit connected to the wire.

pp. 480–481. Generators and Alternating Current.  This explains why rotating a conducting loop rotisserie-style inside a magnetic field induces an alternating potential inside the loop.  This is a consequence and an application of Faraday’s law.

Recommmended workbook exercise:  p. 99, questions 1–2.

Continuing our exploration of electromagnetic induction, we now look at one particular application, transformers, in detail.  Understanding these requires you to draw on many concepts that you have learned throughout the class.

pp. 481–486. Power Production.  The first two parts of this section, “Turbogenerator Power” and “MHD Power,” you can ignore.  We will, however, address the topic of transformers in class.

pp. 483–486. “Transformers.”  The key idea behind the operation of electrical transformers is that an electric potential is induced in a conducting loop when the magnetic field inside the loop changes.  So the essentials of a  transformer are:

• An alternating current powers an electromagnet, creating an oscillating (changing) magnetic field.
• Additional wire loops around the electromagnet have a current induced in them when the magnetic field changes.

This process means that an alternating current in one circuit can set up another alternating current in another circuit!  This may sound confusing, but we actually can make a number of predictions about it using what we already know.

• The induced potential in the “secondary” circuit depends on the number of times the circuit loops around the magnetic field.  We know this from Faraday’s law: if one loop gives a certain potential, two loops will give twice that, three loops will give three times that, and so on.
• The total power induced in the secondary circuit cannot be any greater than the power in the primary circuit.  We know this from the conservation of energy.
• So, if a transformer is perfectly efficient, the power induced in the secondary circuit will be equal to the power in the primary circuit.
• The more voltage that is induced in the secondary circuit, the less current will be in the secondary.  We know this because electric power is (current × potential).  Since there is a limit to the power in the secondary, current and potential must be inversely proportional to each other, so that their product does not exceed the available power.
• In other words, the more turns the secondary circuit loops around the magnetic field, the less current is induced in it!

It gets a bit involved to go further, but there is another important property of these ac transformers: the more times the primary circuit loops around the transformer, the slower its current can change.  This means that the magnetic field it creates also must change more slowly.  The result is less potential induced in the secondary circuit.  Now the reasoning is getting too complicated to follow in words, so we need a formula.  Fortunately, this formula is given in the middle of page 485!

• What is it?

Other vital formulas for understanding how transformers work are given later on page 485.

• What are they?

I recommend doing the “Check Yourself” questions on page 486.  Especially note the explanation in the answer to question 6.  This is a confusing point, and it is explained well.

Recommmended workbook exercise:  p. 100.

pp. 486–487. Self-Induction.  Skip.

p. 487. Power Transmission.  Skip.

p. 488. Field Induction.  Read this; it won’t take long.  It lays the ground work for the topic of light.

p. 489. “Electromagnetic Fields and Cancer” box.  Please read this, even though it is not something we will directly address in class.  It describes a recent example of bad science costing lots of money and scaring lots of people.  Especially consider the last sentence of the essay.

pp. 489–490. In Perspective.  This adds no scientific understanding to your knowledge of electromagnetic phenomena, but it is easy to read, and it puts this information in the context of human history and daily life.  Physics is not just a list of formulas dreamed up by bespectacled men at their desks.  It really is an attempt to find out how the world behaves, and understanding it really changes the course of human events.

Reflection

Think of any type of simple machine you like—levers, multiple pulleys, an inclined plane, a hydraulic jack, different-sized gears turning together, a bicycle, pliers, a fly rod, whatever.  Simple machines are all ways of transforming energy with one set of characteristics into energy with slightly different characteristics.  So, it turns out, are transformers.

• What characteristics are transformed by a simple machine?
• What one characteristic stays the same?
• What about an ac transformer?
• Why are machines and transformers so similar mathematically?  Is it coincidence, or does it reflect a deep physical truth?