What is the significance of the curl of a vector being, Electrical Engineering

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What is the significance of the curl of a vector being

1. What is the determinant expansion for the curl of a vector?

2. What is the significance of the curl of a vector being equal to zero?

3. State Ampere's circuital law in differential form for the simple case of

How is it derived from Ampere's circuital law in integral form?

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Electrical Engineering: What is the significance of the curl of a vector being

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