Proof of Maxwell's Equation Wave Behavior | Maxell Eqn Help

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Discussion Overview

The discussion centers around the proof of wave behavior in magnetic fields as described by Maxwell's equations. Participants explore the derivation and mathematical formulation related to this phenomenon.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant requests a proof that magnetic fields behave like waves according to Maxwell's equations.
  • Another participant notes that the derivation is found in most electromagnetism textbooks, suggesting a standard reference for the proof.
  • A link to an external resource is provided, which may contain relevant information on the topic.
  • A mathematical expression is presented, showing the relationship between the curl of the magnetic field and the electric field, leading to the conclusion that the magnetic field satisfies the wave equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific proof within the thread, and multiple approaches to the derivation are implied but not fully explored.

Contextual Notes

The discussion includes mathematical steps that may depend on specific definitions or assumptions related to Maxwell's equations, which are not fully detailed in the thread.

Who May Find This Useful

Readers interested in electromagnetism, particularly those seeking to understand the wave behavior of magnetic fields as described by Maxwell's equations.

royayash
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hello
Can someone write me the proof, according to Maxwell's equation for magnetic field behaves like a wave??
thanks
 
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There are a number of steps, but the derivation is in most electromagnetism textbooks.
 
∇·B = 0
∇ x B = 1/c ∂E/∂t

∇ x (∇ x B) = 1/c ∂(∇ x E)/∂t
∇∇·B - ∇2B = -1/c22B/∂t2
2B -1/c22B/∂t2 = 0

showing that B satisfies the wave equation.
 
thank u !
 

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