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

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Maxwell's equations demonstrate that the magnetic field behaves like a wave through a series of mathematical derivations. The key equations involved include ∇·B = 0 and ∇ x B = (1/c) ∂E/∂t. By applying vector calculus, it can be shown that ∇ x (∇ x B) leads to the wave equation for B, specifically ∇²B - (1/c²)∂²B/∂t² = 0. This confirms that the magnetic field propagates as a wave. Understanding these derivations is essential for grasping electromagnetic wave behavior.
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/c2∂2B/∂t2
∇2B -1/c2∂2B/∂t2 = 0

showing that B satisfies the wave equation.
 
thank u !
 

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