Electricity and Magnetism

17–122 Electricity and Magnetism

To summarise, ∆N depends on the density of carriers available in the metal and the “up-

stream” volume drifting past the imaginary plane in time ∆t.

∆N = η A ∆x = η A v

d

∆t .

Thus,

∆Q = q η A v

d

∆t , and hence I

av

=

∆Q

∆t

= q η v

d

A .

In a steady state, the instantaneous current is constant and equal to its average value. Thus,

the current in the wire, I, is proportional to q, η, A, and v

d

.

Two comments finish off this chapter.

I Foreshadowing Chapter 18, we observe that the electric current [char ge flux],

like all other fluxes, admits expression as (intensity) · (Area).

I Complicating the picture somewhat, and calling into question ...