Chapter 22 Electromagnetic

Induction

When a coil of wire is in a magnetic field, the magnetic flux Ф is the strength of the field B multiplied by the area of the coil A, Ф = BA.

A potential difference is produced whenever the magnetic flux Ф is changed. This potential difference is in the form of an induced emf ε and is equal to the rate of change in magnetic flux, the magnetic flux divided by the time, ε = ΔФ/Δt or ε = ΔBA/Δt. This is Faraday’s Law of Induction.

Since flux is BA anything that changes B or A will produce an emf. (1) If the strength of the magnetic field is changed, the flux changes and a potential difference is produced.

(2) Area in the field can be changed by moving a coil of wire into or out of a magnetic field. Area in the field can also be changed by rotating a coil of wire about its diameter if the diameter is perpendicular to the field.

Example 1: A loop of wire of area 0.11 m2 is in a 1.0 T magnetic field. If the field strength increases to 4.0 T over a period of 5 seconds, what emf is produced?

Example 2: A loop of wire of area 0.5 m2 is moving into a 0.7 T magnetic field. If it takes 4 seconds for the loop to move from completely outside the field to completely inside the field, what emf is produced?

When an emf is produced using Faraday’s Law a current can be produced. This current will produce its own magnetic field as discussed in the previous chapter. But, what is the direction of the original emf and the conventional current flow?

The direction is such that the magnetic field it produces is opposite the change in flux that produces the emf. This is Lenz’s Law and it is how the direction of the induced current is found. (ε = ΔФ/Δt is usually written with a minus sign, ε = -ΔФ/Δt, to indicate the emf and the current produced are opposite the change in flux.)

To find the direction of the induced current, first determine if the change in flux ΔФ or ΔBA is an increase or a decrease. If it is an increase, the magnetic field produced by the induced current must be in the opposite direction of the original magnetic field.

If the change in flux is a decrease, the magnetic field produced by the induced current must be in the same direction as the original magnetic field. Once the direction of the field produced is known, right hand rule two, rhr-2, is used to find the direction of the induced current produced.

Example 3: A permanent magnet approaches a loop of wire. The external circuit attached to the loop consists of the resistance R. Find the direction of the induced current and the polarity of the induced emf.

Example 4: A conductive loop is entering a magnetic field directed into the plane of the paper. Is the direction of the current produced in the loop clockwise or counterclockwise?

Example 5: This loop continues until it leaves the field. Is the direction of the current produced in the loop clockwise or counterclockwise?

Example 6: What is the direction of the current produced in the loop when it is completely inside the field?

The picture above depicts a counterclockwise current flow produced by change in the magnetic field. Is the magnetic field increasing or decreasing?

An electric generator rotates a coil of wire in a magnetic field. As we have previously seen, this produces an emf in the wire coil and therefore a flow of current. The nature of this rotation causes the direction of the current produced to alternate directions. This is how the AC we use in our homes is produced. It is also how the alternator in your car produces the current to run the electrical devices in the car and recharges the car’s battery.

As we saw last chapter, there is a force on a wire carrying a current in a magnetic field (F= I l B). An electric motor uses this force to produce motion. But Lenz’s Law tells us that this motion of a coil of wire through the magnetic field also produces an induced current.

By Lenz’s Law the emf produced is opposite the direction of the emf that produces the current that turns the motor. Since it is opposite the direction of the source potential this induced emf is called back emf. The net potential difference across the motor is the potential of the source minus the back emf.

Example 7: A motor is connected to a 120 V source. The resistance in the motor coil is 10 Ω and the current produced by the back emf is 11 A. What is the net potential across the motor?

Have you ever wondered why starting a motor like a hair dryer or the motor on an air conditioning system will initially dim the lights in a house, but then the lights return to normal? When the motor is turned on the full 120 V produces a very high current through the resistance. This draws a great deal of power which dims the lights. But after the motor starts spinning, the back emf decreases the net emf, the current drops and the power usage of the motor decreases, and the lights return to their original level.

The structure of DC motors and DC generators is basically the same, so a DC generator can act as a DC motor and a DC motor can act as a DC generator.

Example 8: The armature windings of a DC motor have a resistance of 6 Ω. The motor is powered with 120 V and reaches its full speed against its normal load. The back (counter) emf is 106 V. Calculate the current into the motor at full speed.

A current-carrying coil of wire wrapped around a metal loop produces a magnetic field in the loop. If another coil is wrapped around the other side of the loop it will have an induced emf produced if the field is changing. If the number of loops in each coil is different, the emf is proportionately different in each of the coils. This called a transformer.

There are two types of transformers:

Not really, the two types are step-up and step-down transformers. Step-up transformers increase the voltage, step-down transformers decrease the voltage.

The original coil of wire in a transformer is the coil that comes from the source and is called the primary coil. The coil where the induced emf is produced is called the secondary coil.

In a step-up transformer the primary coil has less loops than the secondary coil. In a step-down transformer the primary coil has more loops than the secondary coil.

The number of loops in the coil is directly related to the voltages: VS/VP = NS/NP. Doubling the number of loops in the secondary coil doubles the output voltage.

The power levels must remain the same and P = IV, so current must change inversely with voltage. VS/VP = NS/NP = IP/IS

Example 9: The number of loops in the primary coil of a transformer is 1200. The secondary coil has 120 loops. If the source voltage is 120 V, (a) what is the resulting voltage? (b) What is the resulting current if the initial current is 0.1 A? (c) What type of transformer is this?