© 2001-2007 shannon w. helzer. all rights reserved. 1 chapter 30 – induction and inductance

© 2001-2007 Shannon W. Helzer. All Rights Reserved. 1

Chapter 30 – Induction and Inductance


Observe what happens when a magnet is passed through a conducting loop. While there was relative motion between the loop and the magnet, we saw that

there was a small current generated in the loop. What did you notice about the generated current when the

direction of the magnet is reversed? The current direction changed. What do you suppose would happen if we inserted the

magnet faster? The faster the relative motion, the more

current is generated within the loop. What do you suppose would happen

if we inserted the South pole of the magnet first?

Again, the current direction changed. There are three ways to have relative

motion between the conductor and the magnetic field: changing magnetic field, changing conductor size, and change of position (conductor or magnetic field source).

Magnetism and Current WS 12 #1-5


Induced emf WS 12 #6-10 In the first of the observed experiments, we discovered that a current is established when there is relative motion between the conduction electrons in the

conducting ring and the magnetic fields of a magnet. We also observed that the amount of induced current is greater when the magnet is moved faster. Additionally, we observed that reversing the direction of motion of the magnet or reversing the poles of the magnet reverses the direction of the produced current. Either way, we had to do work on the system in order to observe this current. This work induced this current; therefore, we call this current induced current. This work done that produced this induced current is known as induced emf. Basically, we can say that changing magnetic fields in the vicinity of electrons causes these electrons to move thereby establishing an induced current. As a result, we can in many ways think of electrons as being

“tiny magnets.”


Observe the behavior of the light bulbs and the ammeter below when the switch is closed and then opened.

What happens when the switch is closed? Bulb one lit up, and bulb two blinked as the ammeter registered a

counterclockwise current. What happens when the switch is opened? Bulb one goes out, and bulb two

blinks again as the ammeter

registers a clockwise current. What do you suppose caused

the behavior we observed?

Magnetism and Current


Induced emf WS 12 #11-14 We previously learned that moving electric charges establish a magnetic field. In the second of the observed experiments, we discovered that a current through one loop established a current in a second parallel loop. However, this current lasted only a short time. Why do you supposed it lasted only a short time. The current established in the second loop only exists when the magnetic field in the first loop is changing. Once this magnetic field stabilizes (stops changing), the electrons in the second loop cease flowing and bulb 2 went out. In the first experiment we concluded that there would be an induced current when there is relative motion between the conducting electrons and the magnetic field. In this experiment we saw that the electrons moved when they

experienced a changing magnetic field. This second experiment shows us another form of

induced emf.


Faraday’s Law of Induction WS 12 #15 & 16 The results of both of these experiments are unified in Faraday’s Law of Induction. This law states that an emf is induced in a wire loop whenever the number of magnetic field lines passing

through that loop changes. This number of magnetic field lines, or the magnetic flux, changes whenever there is relative motion between

the conducting electrons or whenever the magnetic field changes in the vicinity of these conducting electrons. We will begin deriving Faraday’s law below. We can define the magnetic flux in a similar way that we defined the electric flux.

B B dA


Magnetic Flux WS 12 #17-19 Let’s determine the magnetic flux for the case when the uniform magnetic field and

the incremental area vector dA are parallel. Note that dA does not actually represent a physical body. In this problem, it is the area inside the coil of wire. The area in this problem is circular.

B

dA

B B dA

B

cosB B dA B B dA B BA

2B r B


Faraday’s Law of Induction WS 12 #17-19 Faraday’s Law states that an emf is induced in a wire

loop whenever the number of magnetic field lines passing through that loop changes.

We have seen that this number changes when there is relative motion between the magnetic field and the conducting electrons and when the magnetic field itself changes.

Since both of these actions occur over a period of time, this emf () is the rate at which the magnetic field changes.

The “N” in this equation is the number of turns in the coil.

Our previous example has four turns.

BNd

dt

B

dA

B

2B r B

2Nd r B

dt

24dB

rdt


Faraday’s Law Example WS 12 #20 A coil with four turns (r = 0.35 m) lies in a uniform

magnetic field whose magnitude is given by the following equation.

What is the magnitude of the emf 0.4 s after the field is engaged.

23.7 1.1 6B t t

24dB

rdt

dA

B

2

23.7 1.1 6

4d t t

rdt

24 (7.4 1.1)r t


Lenz’s Law WS 12 #21-23 Faraday’s Law enables us to calculate the emf produced between a conductor and a

changing magnetic field. However, his law did not specify the direction of this induced emf. Lenz’s law is used to determine the direction of this induced emf. Lenz’s law states that the magnetic field generated by the induced current opposes

the change in the magnetic field that created the induced current. If the magnetic field of the magnet is increasing then the magnetic field generated

by the induced current acts to oppose this increase. If the magnetic field of the magnet is decreasing then the magnetic field generated

by the induced current acts to oppose this decrease.

MB

ICB


Is the current through the conducting ring below clockwise or counter clockwise when the magnet is inserted?

Explain your answer. The magnet moves into the ring with its North pole first. As a result, the magnetic field impacting the ring acts out of the

plane of the board. Therefore, the induced magnetic field acting against the

magnetic field of the bar magnet must act into the

board inside the ring and out of the

board on the outside of the ring. Using our right hand rule, we see that

the induced magnetic field within the

ring can only be established by a

clockwise current.

Lenz’s Law – Magnetism and Current


What is the direction of the induced magnetic field in the front coil when the switched is closed?

The battery would produce a clockwise current within the front loop. Would the magnetic field produced inside the front loop act into or out of the

plane of the board? In which direction would the induced magnetic field in the

back loop act? In which direction would the

current flow through this

back loop?

Magnetism and Current WS 12 #25

I


Faraday’s Law Example with Lenz’s Law WS 12 #26-28 A coil with four turns (r = 0.35 m) lies in a uniform

magnetic field whose magnitude is given by the following equation.

What is the magnitude of the emf 0.4 s after the field is engaged.

In which direction does the emf act? Lenz’s law states that the magnetic field generated by

the induced current opposes the change in the magnetic field that created the induced current.

In order to find the direction of the induced emf, point your right thumb in

the direction of BIC and curl your fingers. The induced current is in the direction

of your right fingers.

B

ICB


WS 12 #29-32 A conducting ring made of an elastic material is placed in a uniform magnetic field of 0.067 T. The ring is stretched until it has a radius of 15.55 cm. What is the magnetic flux through the ring? It is then released and shrinks at 43.5 cm/s until its size is reduced by 50%. What is the emf produced at the instant the ring begins to shrink? Draw the magnetic field produced by the induced current. In which direction does this induced current flow? What is the new magnetic flux through the ring?

B B dA

BNd

dt


Slide Wire Generator WS 12 #33 & 34 Two long, horizontal wires are connected to a LED as shown. These wires lie in a uniform magnetic field. A third wire is placed vertically across the first two. This wire roles along the first two at a constant velocity v. Derive an equation for the magnetic flux within the rectangle formed by the edge of the diode housing and the three wires. What is the magnitude of the induced emf? What is the direction of the induced current?

dA


Slide Wire Generator WS 12 #33 & 34 Derive an equation for the magnetic within the rectangle formed by the edge of the

diode housing and the three wires. What is the magnitude of the induced emf?

dA

A hw

A h vt

A hvt

dA hvdt

B Bhvdt Bd Bhvdt

BdBhv

dt

B B dA


topI

WS 12 #35 Three parallelograms are placed a distance of L from a current carrying wire

carrying a constant current of i. The middle parallelogram is not centered on the wire. How do the currents generated in the three loops compare to one another (equal,

greater than, less than, zero, ….)? Hint 1: Consider symmetry.

A CiB

topI

botI botI


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a a B

dA

B

v

v

v

v


v

A B C


WS # A circular conducting ring undergoes expansion growing to 150 % its room

temperature size. During this process, a uniform magnetic field induces a counterclockwise current

within the ring.

i


v


a a

B B dA

© 2001-2007 shannon w. helzer. all rights reserved. 1 chapter 30 – induction and inductance

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