Divergence Theorem: Explaining in Simple Words

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The divergence theorem relates a volume integral to a surface integral, illustrating how the net flux of a vector field through a closed surface corresponds to the behavior of the field within the volume. It signifies that the total "outflow" of a vector field from a volume is equal to the sum of the divergence within that volume. This concept can be simplified by understanding divergence as the rate of change of volume at a point. Essentially, it connects the flow of a field across a boundary to its behavior inside the volume. The theorem is crucial in fields like fluid dynamics and electromagnetism for analyzing field behaviors.
wasi-uz-zaman
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i want to know the physical significance of divergence theorem i.e how volume integral changes to surface integral - how can i explain in simple words.
 
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wasi-uz-zaman said:
HI experts
i want to know the physical significance of divergence theorem i.e how volume integral changes to surface integral - how can i explain in simple words.

Hi!
Basically, the divergence can be thought of as the (relative) rate of change of volume.

But, we may do this in another way, namely by calculating the net flux across the original surface.
 
thanks alot
 

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