Question #214798

prove : div cur l f =0

Expert's answer

We introduce the vector differential operator "\\nabla" (“del”) as

Then for the vector field "\\vec F"

"div\\vec F=\\nabla \\cdot\\vec F"

The cross product "\\nabla \\times\\vec F" is perpendicular to both "\\nabla" and "\\vec F."

Hence for any vector field "\\vec F"

"\\nabla\\cdot(\\nabla\\times\\vec F)=0"Therefore for any vector field "\\vec F"

"div(curl \\vec F)=\\nabla\\cdot(\\nabla\\times\\vec F)=0"

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