Maxwell's/Faraday Law Concern Propagation of Induced Fields

In summary: So, Maxwell's equation predicts that at that instant, there should be some nonzero integral of the E field at some radius R away from the newly introduced B field?Is Maxwell's equation wrong in this area?
  • #1
Electric to be
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The integral form of Maxwell's equation pertaining to induced electric fields is:

∮E(t0)⋅dℓ= −dΦ(t)/dt|t=t0Say for a long time, in some circular region there has been no B or E fields present. Then, there is a sudden constant increase of B field introduced in the middle. I know that information cannot propagate faster than the speed of light, but doesn't Maxwell's equation predict that at that instant, there should be some nonzero integral of the E field at some radius R away from the newly introduced B field? Is Maxwell's equation wrong in this area? This equation written explicitly doesn't somehow tell me that, "Oh there will be a field there, but only after a few instants once there has been sufficient time for that information to spread" haha.

Or does the integral form somehow not hold? (I thought integral and differential form are equivalent, by Stoke's/Divergence Theorem)

Thanks for any help in clearing up this doubt.
 
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  • #2
Not sure if I'm reading the question correctly, but...

$$\nabla \times E(x,y,z,t) = -\frac{\partial B(x,y,z,t)}{\partial t}$$

Which says the curl of the electric field at one instant in time at some point is proportional to the time rate of change of the magnetic field at the same point and instant in time.

Does that clear it up? Can you maybe reword if not.
 
  • #3
Student100 said:
Not sure if I'm reading the question correctly, but...

$$\nabla \times E(x,y,z,t) = -\frac{\partial B(x,y,z,t)}{\partial t}$$

Which says the curl of the electric field at one instant in time at some point is proportional to the time rate of change of the magnetic field at the same point and instant in time.

Does that clear it up? Can you maybe reword if not.

So this is the differential form of the equation that I wrote. However, I simply provided the integral form and a situation which seems to violate it. (They are identical by Stoke's theorem)

However, I think I figured it out. At least this is my guess. It isn't possible to provide a constant changing flux without also having the electric field. By this I mean even if I try to provide a constant rate of change of flux, it will stay zero until the wave propagates to the radius.
 
  • #4
Electric to be said:
Then, there is a sudden constant increase of B field introduced in the middle.
This type of B field is not possible. If you think about flux lines they must all be closed loops. To get a net flux through the surface, one part of the loop must propagate until it crosses the edge. That only happens at the speed of light.
 

FAQ: Maxwell's/Faraday Law Concern Propagation of Induced Fields

1. What is Maxwell's Law Concerning Propagation of Induced Fields?

Maxwell's Law Concerning Propagation of Induced Fields, also known as Maxwell-Faraday Law, is one of the four Maxwell's equations that describe the behavior of electric and magnetic fields. It states that a changing magnetic field induces an electric field, and vice versa. This law forms the basis of electromagnetic induction, which is used in various technologies such as generators and transformers.

2. How does Maxwell's Law relate to Faraday's Law?

Maxwell's Law and Faraday's Law are closely related and are often referred to as one law, the Maxwell-Faraday Law. This is because Faraday's Law of Induction, which states that a changing magnetic field induces an electric field, was one of the key components used by Maxwell to formulate his law of electromagnetic induction.

3. What is the importance of Maxwell's Law in understanding electromagnetic fields?

Maxwell's Law is crucial in understanding the behavior of electric and magnetic fields and their interaction with each other. It explains how a changing magnetic field can create an electric field, and how an electric field can create a magnetic field. This law is also essential in understanding the propagation of electromagnetic waves, which are used in various forms of communication and technology.

4. Can Maxwell's Law be applied to all types of electromagnetic fields?

Yes, Maxwell's Law can be applied to all types of electromagnetic fields, including static and dynamic fields. This law is a fundamental principle of electromagnetism and applies to all types of electromagnetic phenomena.

5. How is Maxwell's Law used in practical applications?

Maxwell's Law is used in various practical applications, such as generators, transformers, and electric motors. It is also used in the development of technologies that rely on electromagnetic waves, such as radio, television, and cell phones. Additionally, this law is essential in understanding the behavior of light, which is an electromagnetic wave.

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