Why is the divergence of a curl always zero?
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Hey.
Here is your answer.
Consider as an example the magnetic field B⃗ B→:
The magnetic field is defined as the curl of the potential vector A⃗ A→.
Maxwell's equations tell us that the divergence of the magnetic field is always 0, so this is a physical example of a vector field (A⃗ A→) whose divergence of its curl is zero, but with its curl nonzero.
Notice that here the fact that the divergence of the magnetic field is zero does not depend on whether it expands or shrinks, in fact, it is always zero because the magnetic field lines are always closed.
Thanks.
Here is your answer.
Consider as an example the magnetic field B⃗ B→:
The magnetic field is defined as the curl of the potential vector A⃗ A→.
Maxwell's equations tell us that the divergence of the magnetic field is always 0, so this is a physical example of a vector field (A⃗ A→) whose divergence of its curl is zero, but with its curl nonzero.
Notice that here the fact that the divergence of the magnetic field is zero does not depend on whether it expands or shrinks, in fact, it is always zero because the magnetic field lines are always closed.
Thanks.
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