5.0 Unit 5 Overview: Electromagnetism

Unit 5 covers the topic of electromagnetism, which is the study of the relationship between electrically charged particles and magnetic fields. It includes topics such as:

1. Electric charge and electric fields
2. Coulomb's law and electric potential
3. Electric circuits and Ohm's law
4. Magnetic fields and magnetic forces
5. Electromagnetic induction
6. AC and DC circuits
7. Maxwell's equations

In this unit, you will learn about the fundamental principles of electromagnetism, how electric and magnetic fields interact with each other, and how these principles are used in modern technology such as motors, generators, transformers, and communication devices. You will also learn about the properties of electromagnetic waves and how they propagate through space. Finally, you will gain an understanding of the relationship between electromagnetism and relativity.

5.1 Electromagnetic Induction (Including Faraday’s Law and Lenz’s Law)

Electromagnetic induction is the process of generating an electromotive force (EMF) by changing the magnetic field around a conductor. This phenomenon was first discovered by Michael Faraday, who found that a changing magnetic field can induce an electrical current in a nearby conductor.

Faraday's Law states that the magnitude of the EMF induced in a circuit is directly proportional to the rate of change of the magnetic flux through the circuit. The magnetic flux is defined as the product of the magnetic field strength and the area of the loop that the field passes through. This means that if the magnetic field strength or the area of the loop changes, then the induced EMF will change as well.

Lenz's Law is another important principle of electromagnetic induction. It states that the direction of the induced current in a circuit is always such that it opposes the change that produced it. This means that if the magnetic field is increasing, the induced current will flow in a direction that generates a magnetic field that opposes the increasing field. If the magnetic field is decreasing, the induced current will flow in a direction that generates a magnetic field that opposes the decreasing field.

One common application of electromagnetic induction is in electric generators, which use the principle of a changing magnetic field to generate an electric current. Transformers also use electromagnetic induction to transfer electrical power from one circuit to another through a changing magnetic field.

5.2 Inductance (Including + LR circuits)

Inductance is a property of a conductor that describes the ability of the conductor to store energy in a magnetic field. When an electrical current flows through a conductor, it generates a magnetic field around the conductor. This magnetic field, in turn, induces a back EMF in the conductor, which opposes the current flow.

The amount of inductance of a conductor is determined by its physical properties, such as the number of turns in a coil, the cross-sectional area of the coil, and the permeability of the surrounding material. The unit of inductance is the henry (H), and it is represented by the symbol "L".

In an LR circuit, which is a circuit that contains an inductor and a resistor in series, the inductor causes the current to lag behind the voltage due to the back EMF that it produces. This lag causes the circuit to behave differently from a simple resistor circuit. The rate of change of the current is proportional to the voltage across the resistor, and also to the voltage across the inductor, which is given by Ldi/dt, where i is the current and t is time.

The behavior of an LR circuit can be analyzed using differential equations, and the time constant of the circuit is given by the ratio of the inductance to the resistance. This time constant represents the time it takes for the current in the circuit to reach 63.2% of its final value after a sudden change in voltage is applied.

5.3 Maxwell’s Equations

Maxwell's equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields and their relationship to electric charges and currents. These equations were developed by James Clerk Maxwell in the 19th century and are the foundation of the modern theory of electromagnetism.

The four Maxwell's equations are:

1. Gauss's law for electric fields: The electric flux through a closed surface is proportional to the charge enclosed within the surface.
2. Gauss's law for magnetic fields: The magnetic flux through a closed surface is always zero.
3. Faraday's law of electromagnetic induction: The EMF induced in a closed loop is equal to the negative of the time rate of change of the magnetic flux through the loop.
4. Ampere's law with Maxwell's correction: The circulation of the magnetic field around a closed loop is proportional to the sum of the electric current passing through the loop and the time rate of change of the electric field in the loop. These equations show the close relationship between electric and magnetic fields and provide a way to understand the behavior of electromagnetic waves, such as light. They are used extensively in the design of electrical and electronic devices, such as antennas, motors, transformers, and generators. They also form the basis for the study of many areas of modern physics, including quantum mechanics and relativity.

In summary, Maxwell's equations are essential to understanding the behavior of electric and magnetic fields and their relationship to electric charges and currents. They have broad applications in many areas of science and technology, and continue to be a subject of active research and study.

Questions for Review

• What is electromagnetic induction and how does it relate to Faraday's Law and Lenz's Law?
• What is inductance, and how is it related to the storage of energy in a magnetic field?
• How does an LR circuit differ from a simple resistor circuit, and what is the time constant of the circuit?
• What are Maxwell's equations and how do they describe the behavior of electric and magnetic fields?
• How are the principles of electromagnetism used in the design and operation of electrical and electronic devices such as motors, transformers, and generators?
• What is the relationship between electromagnetism and other fields of physics, such as quantum mechanics and relativity?
• How do electromagnetic waves propagate through space, and what are their properties and applications?
• How do magnetic materials behave, and how do they relate to the principles of electromagnetism?
• What are some practical applications of the principles of electromagnetism in everyday life, and in science and technology?