# Magnetic Induction: Exploring Induced EMF & Faraday's Law

• syang9
In summary, the induced emf in a circular coil with a constant rate of increase in the magnitude of a B-field can be calculated by removing the B-field from the flux integral, as the integral is taken over an area and the magnetic field is constant throughout that area. The induced emf is then determined by the rate of change of the flux with time.
syang9
induced emf!

Hello,

I am studying magnetic induction, induced emf, and faraday's law, that sort of thing. My book gives an example where the magnitude of a B-field is increasing at constant rate through an axis of a circular coil with N number of turns and a certain radius r, find the induced emf in the coil. However, in the solution, it says that the B-field is constant, and can be removed from the flux integral! How can this be possible, if it is increasing with time?

Thanks,

Stephen

Last edited:
syang9 said:
Hello,

I am studying magnetic induction, induced emf, and faraday's law, that sort of thing. My book gives an example where the magnitude of a B-field is increasing at constant rate through an axis of a circular coil with N number of turns and a certain radius r, find the induced emf in the coil. However, in the solution, it says that the B-field is constant, and can be removed from the flux integral! How can this be possible, if it is increasing with time?

Thanks,

Stephen
The flux integral is an integral over an area at each moment in time. If the magnetic field is the same throughout the area enclosed by the coil, it is a constant for that integral. The result of the calculation will be a flux that depends on time. The rate of change of that flux with time gives you the induced emf.

syang9 said:
Hello,

I am studying magnetic induction, induced emf, and faraday's law, that sort of thing. My book gives an example where the magnitude of a B-field is increasing at constant rate through an axis of a circular coil with N number of turns and a certain radius r, find the induced emf in the coil. However, in the solution, it says that the B-field is constant, and can be removed from the flux integral! How can this be possible, if it is increasing with time?

Thanks,

Stephen
The flux is the integral of the magnetic field over an area at each moment in time. If the magnetic field is the same throughout the area enclosed by the coil, it is a constant for this integral. The result of the calculation will be a flux that depends on time. The rate of change of that flux with time gives you the induced emf.

## 1. What is magnetic induction?

Magnetic induction is the process by which a changing magnetic field induces an electric field in a conductor, resulting in the production of an electric current.

## 2. How does magnetic induction work?

Magnetic induction works through Faraday's law, which states that a changing magnetic field will induce an electromotive force (EMF) in a conductor. This EMF will cause electrons to flow, creating an electric current.

## 3. What is Faraday's law?

Faraday's law is an electromagnetic principle that describes the relationship between a changing magnetic field and an induced electric field. It states that the magnitude of the induced EMF is directly proportional to the rate of change of the magnetic field.

## 4. What are some real-world applications of magnetic induction?

Magnetic induction has many practical applications, including power generation in generators and transformers, wireless charging, and induction heating. It is also used in various technologies such as electric motors, speakers, and magnetic levitation trains.

## 5. How does magnetic induction relate to electromagnetic waves?

Magnetic induction is closely related to electromagnetic waves as both involve the interaction between electric and magnetic fields. In fact, electromagnetic waves are created through the process of magnetic induction, as a changing electric field induces a magnetic field, which then induces an electric field, and so on.

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