Electricity and Magnetism

Chapter 18

Electric Current Density, Ohm’s Law, and Resistance

In the last chapter, a formula for the electric current in a wire,

I = q η v

d

A ,

was derived, and much ado was made about its interpretation as charge flux. In the above

expression, q η is the free electric charge density, v

d

is the drift speed [assumed to be uniform],

and A is the cross-sectional area. Strictly speaking, a proper expression of flux accounts for

the vector nature of two of the above quantities, and so a more general formula is

I = q η ~v

d

·

→

A .

This expression for the current suffices for uniform drift velocities and planar surfaces. IF

the drift velocity field is not uniform OR ...