What gives rise to non-ballistic behavior?
E-field in conductor (resistor) provided by a battery
Charges are put in motion, but scatter in a very short time from things that get in the way
- it’s crowded in side that metal
- defects, lattice vibrations (phonons), etc
- Typical scattering time t = 10-14 sec
- charges ballistically accelerated for this time and then randomly scattered
- average velocity attained in this time is v = eEt/m
- current density is J = env so current is proportional to E which is proportional to Voltage
- OHM’s LAW J = (e2nt/m)E or J = sE s = conductivity