Current, Ohm’s Law, Etc.

The Continuity Equation for Steady State Currents Currents and current densities are constant in time – steady state. The flux of out of any closed surface must be zero.

For steady state situation

Problem 4 Two wires having different resistivities ρ 1 and ρ 2 and equal cross sections, a, are connected end to end. Their lengths are l 1 and l 2. If a battery is connected to this system such that a potential difference of V is maintained between the ends, a)What will be the current densities in the wires? b) What will be the potential difference across each wire? c)Will there be any charge on the surface where the wires are connected?

Exercise 5 Consider a cylindrical shell, inner radius a and outer radius b. It is made of material with resistivity ρ. Suppose a current can be made to flow out from the inner surface to the outer. What would the resistance be for this current?

Drift velocity