Zero curl and gradient of some scalar potential

redredred
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Can someone help me intuitively understand why if a field has zero curl then it must be the gradient of a scalar potential?

Thanks!
 
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redredred said:
Can someone help me intuitively understand why if a field has zero curl then it must be the gradient of a scalar potential?

Thanks!

If the curl is zero the field does not rotate so the field lines look like gradient flows.
 

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