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gradient,div and curl

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electronics_kumar

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gradient div

in field theory,
gradient of scaler will give vector field
divergence of vector will give a scaler field
curl of vector will give vector field.

but i want to know what will happen if it is curl of gradient
curl of divergence
gradient of curl
gradient of div
div of curl
div of grad

but some of cases will yield result as zero? what will be other non zerocases?
what are they ? why it is ?
 

curl and gradient

Hello;
Also read vector analysis sections of this book:

Field and Wave Electromagnetics
D. K. Cheng
 

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