I first learned Maxwell's equations in their integral form before I was introduced to the differential form, i.e. w/curl & divergence. As I understand, in order to derive the curl form from the integral form, apply Stokes Theorem to the integral form of ∫(closed)E⋅dl=-d/dt[∫(closed)B⋅dA], and you first need to commute the 'd/dt' through the integrand, where it becomes it a partial derivative: ∫(closed)E⋅dl=-∫(closed)[∂B/∂t⋅dA] It is this commutation which gives it the form of Stoke's Theorem, which is how we derive curl E = -∂B/∂t. What I don't understand is how this commutation is permissible unless we know the limits of integration on the right side intregand are constant with respect to time... and ... without this commutation through the integrand, it doesn't really take the form of Stoke's Theorem, does it? In short, I wonder of this curl equation has some limitations: Imagine the B vector is constant everywhere with respect to time, and there is a shrinking loop of wire in the area. Well, according to the relation curl E = -∂B/∂t, we ought to expect that curl E is zero everywhere ... but it (intuitively?) simply cannot be zero everywhere ... at least not if there is a non-zero integral of E around the loop, correct?