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Topic | Discussion | Learning Aids
Electromagnetic induction | 22.1 INDUCED EMF AND INDUCED CURRENT Electromagnetic induction is the phenomenon in which an emf is induced in a piece of wire or a coil of wire with the aid of a magnetic field. The emf is called an induced emf, and any current that results from the emf is called an induced current. |
| 22.2 MOTIONAL EMF An emf E is induced in a conducting rod of length L when the rod moves with a speed v in a magnetic field of magnitude B, according to |
Motional emf |

| (22.1)

| Equation 22.1 applies when the velocity of the rod, the length of the rod, and the magnetic field are mutually perpendicular. |
Conservation of energy | When the motional emf is used to operate an electrical device, such as a light bulb, the energy delivered to the device originates in the work done to move the rod, and the law of conservation of energy applies. |
| 22.3 MAGNETIC FLUX The magnetic flux that passes through a surface is |
Magnetic flux |

| (22.2)

| where B is the magnitude of the magnetic field, A is the area of the surface, and is the angle between the field and the normal to the surface. |
| The magnetic flux is proportional to the number of magnetic field lines that pass through the surface. |
| 22.4 FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION Faraday’s law of electromagnetic induction states that the average emf E induced in a coil of N loops is |
Faraday’s law |

| (22.3)

| where is the change in magnetic flux through one loop and is the time interval during which the change occurs. Motional emf is a special case of induced emf. |
Lenz’s law | 22.5 LENZ’S LAW Lenz’s law provides a way to determine the polarity of an induced emf. Lenz’s law is stated as follows: The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change. This statement is a consequence of the law of conservation of energy. |

Use Self-Assessment Test 22.1 to evaluate your understanding of Sections 22.1, 22.2, 22.3, 22.4 and 22.5 .

| 22.7 THE ELECTRIC GENERATOR In its simplest form, an electric generator consists of a coil of N loops that rotates in a uniform magnetic field . The emf produced by this generator is |
Emf of a generator |

| (22.4)

| where A is the area of the coil, is the angular speed (in rad/s) of the coil, and is the peak emf. The angular speed in rad/s is related to the frequency f in cycles/s, or Hz, according to . |
| When an electric motor is running, it exhibits a generator-like behavior by producing an induced emf, called the back emf. The current I needed to keep the motor running at a constant speed is |

| (22.5)

Back emf of a motor | where V is the emf applied to the motor by an external source, E is the back emf, and R is the resistance of the motor coil. |
| 22.8 MUTUAL INDUCTANCE AND SELF-INDUCTANCE Mutual induction is the effect in which a changing current in the primary coil induces an emf in the secondary coil. The average emf induced in the secondary coil by a change in current in the primary coil is |
Emf due to mutual induction |

| (22.7)

Mutual inductance | where is the time interval during which the change occurs. The constant M is the mutual inductance between the two coils and is measured in henries (H). |
| Self-induction is the effect in which a change in current in a coil induces an average emf E in the same coil, according to |
Emf due to self-induction |

| (22.9)

Self-inductance | The constant L is the self-inductance, or inductance, of the coil and is measured in henries. |
| To establish a current I in an inductor, work must be done by an external agent. This work is stored as energy in the inductor, the amount being |
Energy stored in an inductor |

| (22.10)

| The energy stored in an inductor can be regarded as being stored in its magnetic field. At any point in air or vacuum or in a nonmagnetic material where a magnetic field exists, the energy density, or the energy stored per unit volume, is |
Energy density of a magnetic field |

| (22.11)

| 22.9 TRANSFORMERS A transformer consists of a primary coil of Np turns and a secondary coil of Ns turns. If the resistances of the coils are negligible, the voltage Vp across the primary and the voltage Vs across the secondary are related according to the transformer equation: |
Transformer equation |

| (22.12)

Turns ratio | where the ratio Ns/Np is called the turns ratio of the transformer. |
| A transformer functions with ac electricity, not with dc. If the transformer is 100% efficient in transferring power from the primary to the secondary coil, the ratio of the secondary current Is to the primary current Ip is |

| (22.13)

Use Self-Assessment Test 22.2 to evaluate your understanding of Sections 22.7, 22.8 and 22.9 .

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