The Partial Derivative
The Plus (+) Sign in Ampere's Law
You probably know what addition is, in terms of the (+) sign for numbers:
There are a couple things that make this addition sign worth talking about. The first is that this is a vector addition, which means the addition is componentwise. To make this explicit, let's start with two 3-dimensional vector fields, let's call them A and B. Then the addition of these two components is shown in Equation :
Equation  is pretty straightforward, and since the units of Ampere's Law are Amps/meter^2, this plus sign relates components with these values.
Finally, the last thing of importance is that physically, this plus sign means that there are two independent phenomena that can give rise to the same thing - namely the left side of Ampere's law, the curl of the magnetic field. This means that the effect of current density J and a time-varying electric flux density both give rise to the same thing. This is very interesting as it explains the equivalence of current density and change in electric flux density - which is also how electric current can flow through a circuit which includes a series capacitor. For more information, see Ampere's Law.
This page on the vector addition, particularly in relation to Ampere's Law of Maxwell's Equations is copyrighted. Copyright www.maxwells-equations.com, 2012.