so we have the identity(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\nabla\times\nabla\phi = 0[/itex]

and from Maxwell's equations we have

[itex]\nabla\times \textbf{E} = -\frac{d\textbf{B}}{dt}[/itex]

But we also have that

[itex]\textbf{E} = -\nabla\phi[/itex]

So the problem I'm having is this

[itex]-\textbf{E} = \nabla\phi[/itex]

which i substitute into the identity

[itex]\nabla\times -\textbf{E} = - ( \nabla\times\textbf{E} ) = 0[/itex]

But this should be

[itex]\nabla\times - \textbf{E} = \frac{d\textbf{B}}{dt}[/itex]

according to maxwell's equations, not zero

which is why im getting confused

i think there is a good chance ive done somehing silly, i just need someone to point it out

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# Vector calculus identities and maxwell equations

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