//Well, our Italiano professor's spoken English is... a little hard to understand...

//In this chapter we discuss charge?in motion.

4.1 Electric current and current density

An electric current is charge in motion. The electric current in a wire is the amount of charge passing through it per unit time.

It can also be expressed as the flux of electric current density:

and electric current density is determined by the density of charge carriers?, the?amount of charge on each carrier , and the average speed of the carriers .

4.2 Steady currents and?charge conservation

We've mentioned conservation of charge:

And in a steady or stationary current system, we know the charge density can't grow infinite,

4.3 Electrical conductivity and Ohm's law

We know in electrostatic cases ?in a conductor must be 0. But when an electric field? exists inside a conductor and pushes free charges (electrons) inside, the result is an electric current in the direction of?. (And that's not electrostatic case.)

That's the differential form of Ohm's law.? is called the conductivity of the material.

We're more familiar to its original form:

Generally the rule above should be written as

Where the nine factors make up?a tensor, which here is just a matrix.

And this matrix must be symmetric:?,?for example.

Further more, by a suitable orientation of the xyz axis, the tensor will be diagonal:

（電導(dǎo)率張量一定是對(duì)稱的，因此可以對(duì)角化，當(dāng)選取該材料晶體主軸時(shí)，電導(dǎo)率張量必為對(duì)角的。）

To calculate the resistance R of a rod, we have

where? is the total length of the resistance, and ?is its cross-sectional area of the rod.