Why Is Potential Constant When E-Field Is 0?

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When the electric field (E-field) is zero in a region of space, the electric potential remains constant because potential is defined as the negative integral of the electric field. If E equals zero, the integral results in a constant value for potential. According to Maxwell's equations, a zero curl of the electric field indicates that it can be expressed as the gradient of a scalar potential. Therefore, changing the potential by a constant does not affect the electric field, which remains unchanged. Ultimately, the potential can be any constant value, including zero, in regions where the electric field is zero.
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if the E-field is zero in a region of space, why i the potential always a constant?

For example:

V=-\int E dl

if E = 0, then wouldn't the potential automatically be zero?
 
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From Maxwell equations for stationary fields: \nabla \times E = 0
it follows that E is gradient of some field. So we write E = -\nabla \phi.
You see that if you change phi for a constant results the same field E.
All it counts are the differences in phi. So potential can also be zero.
 

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