G L Pollack and D R Stump Electromagnetism 1 7. Electric Current Chapter Summary Current is flow of charge: If charges q with number density n move with mean velocity  v  then the current density is J = q n  v . (Derive this result; how much charge passes an area dA in time dt?)

G L Pollack and D R Stump Electromagnetism 2 The continuity equation expresses conservation of charge. In differential form, in integral form, (Show that these equations are equivalent, and explain why they describe conservation of charge.) Conservation of charge is a truly fundamental aspect of nature, ultimately coming from the properties of elementary charged particles—leptons and quarks.

G L Pollack and D R Stump Electromagnetism 3 Ohm’s Law The most familiar statement of Ohm’s Law is that the current I in a resistor is proportional to the potential drop V, V = IR and the constant R is the resistance. A more profound statement is that the current density in a conductor is proportional to the electric field, J(x) =  E(x) and  is the conductivity of the material. The relation between R and  is that the resistance of a wire of length l and area A is R=  l/A where  =1/ . Conductivity is an intrinsic property of the material; resistance depends also on the geometry of the conductor.