Physical intepretation of derivative in Maxwell equation?

[DunWorry]

I'm having a little difficulty understanding the use of derivatives in Maxwell's equations. Eg. $\oint E . dl$ = - $\frac{d\varphi_{B}}{dt}$ this says that a changing magnetic flux in time, produces a potential difference (and electric field) in space? I noticed that its a full derivative, and its dt. Whats the significance of this? why would it be wrong if it was magnetic flux changing in space or something?

This can be re-written as $\nabla x E$ = - $\frac{dB}{dt}$ So a curling electric field in space, produces a changing magnetic field that varies in time? how come there is no space dependence on the magnetic field? like in an EM wave the magnetic field doesn't just stay in one spot and change its magnitude, it propagates with the electric field.

Perhaps its my understanding of curl? or does it mean the curl of the electric field at a certain point in the field, produces a changing magnetic field at that point also?

I'm not sure =D
Thanks!

 

[phyzguy]

You have it backwards. It's not that "a curling electric field in space, produces a changing magnetic field that varies in time", it's that a time-varying magnetic field produces an electric field with non-zero curl. The right-hand side is the source of the field on the left-hand side.

 

[meBigGuy]

The equations work both ways.

B represents a vector magnitude and direction, so it's spatial characteristics are included. The dt derivative indicates how it changes with time.