Faraday's law for an infinite magnetic field slab

• ehrenfest
In summary, we have an infinite slab of uniform magnetic field that extends out to infinity in two directions (x and y) and points in the third direction (z). The original problem is asking for the electric field induced by Faraday's Law at any point inside the slab. It is determined that the electric field must be radially symmetric in a plane parallel to the slab planes, but this would violate Faraday's Law. The confusion lies in the definition of the infinite slab and its dimensions.
ehrenfest

Homework Statement

The magnitude of an infinite slab of uniform magnetic field is increased. What is the electric field induced by Faraday's Law

Homework Equations

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$

The Attempt at a Solution

Choose any point inside the slab. Because the magnetic field is radially symmetric about that point, the electric field must also be radially symmetric. By radially symmetric, I mean radially symmetric in a plane parallel to the slab planes. But if you choose any other point, the electric field must also be radially symmetric about that point. This can only happen if the electric field points perpendicular to the slab planes. But that violates Faraday's law...I'm confused.

ehrenfest said:
.I'm confused.

So am I...what do you mean by "an infinite slab of uniform magnetic field"?...Does the slab extend to infinity in all three dimensions or just 2 or 3? Are you told which direction the uniform field point in?

Please write out the complete original problem statement, word for word.

Its a problem I thought up myself. The magnetic field extends out to infinity in two directions (say x and y) and it points in the third direction (z).

1. What is Faraday's Law for an infinite magnetic field slab?

Faraday's Law for an infinite magnetic field slab is a principle in electromagnetism that describes the relationship between a changing magnetic field and the induced electric field in a slab of infinite thickness. It states that the induced electric field is proportional to the rate of change of the magnetic field and is perpendicular to both the magnetic field and the direction of change.

2. How does Faraday's Law for an infinite magnetic field slab differ from the original Faraday's Law?

The original Faraday's Law, which is a fundamental principle in electromagnetism, states that the induced electromotive force (EMF) in a closed loop is equal to the negative of the rate of change of the magnetic flux through the loop. Faraday's Law for an infinite magnetic field slab is a specific application of this principle for an infinite slab of material with a uniform magnetic field.

3. What is the significance of an infinite magnetic field slab in Faraday's Law?

An infinite magnetic field slab is used in Faraday's Law to simplify the calculations and to demonstrate the principle in a more practical manner. This idealized setup allows for the magnetic field to be considered constant throughout the slab, making the calculations easier and more accurate.

4. How is Faraday's Law for an infinite magnetic field slab used in real-world applications?

Faraday's Law for an infinite magnetic field slab has numerous real-world applications, such as in the design of induction motors and generators, which use the principle to convert mechanical energy into electrical energy. It is also used in the development of magnetic sensors and in the study of electromagnetic fields in materials.

5. What are the limitations of Faraday's Law for an infinite magnetic field slab?

Faraday's Law for an infinite magnetic field slab is only valid for an idealized setup of an infinite slab with a uniform magnetic field. In real-world applications, the magnetic field is rarely uniform, and the slab is never truly infinite. Additionally, the law does not account for factors such as resistance and energy losses, which can affect the accuracy of the calculations.

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