Stokes Theorem

$U = int (C) (E*d L)$

$Phi = int (S) (B*d A)$

$U = -d(Phi)/d t$

$int(C) (E*d L) = -d*[int(S) (B*d A)] = int (S) (-dB/d t*d A)$ (1)

stokes theorem for function $f$ is

$int(C) (f*d L) =int (S) curl(f) *d A$

therefore (1) becomes

$int_{(S)} (curl(E)*d A)=int_{(S)} ((-dB/d t)*d A)$

thus

$curl(E) =-dB/d t$