9780030839931, Chapter 1, Problem 2P

Prévia do material em texto

Chapter Problem 2P Problem Heating Consider metal uniform temperature static uniform electric electron experiences a collision and then after time second collision model energy is not for the mean electron emerging collision does not depend energy that electron quired from the field since the receding collision (assumption 4.page (a) Show that average energy lost second two collisions separated time average over directions which the electron emerged from the (b) Show, using the result Problem that average energy loss to the per collision and hence that the average loss centimeter per Deduce that the power wire length and cross section where is the current flowing and resistance the wire Step solution Step (a) assume represents the velocity vector electron then the energy the electron immediately after collision Also electron moves under the of force cE for time Therefore the velocity of the electron due this Here, the velocity vector of the electron due F the mass of the and is the charge of the electron Anonymous understand why energy about kinetic where the potential energy? Anonymous You can consider doing the rest of this calculation including potential energy but since the potential energy does not change anywhere ghout experiment the potential energy term will stil cancel nonetheless Hope Step collision during this time the resulting energy Substitute Step The average energy lost the electron after time given Substitute note that the average of velocity (v) would be accounts the there always an electron moving the opposite direction with the same velocity Therefore one can write the average energy gained the electron The mag itude of the average energy AE Therefore average energy lost the the second two separated by time Step (b) The average over intervals between can be alculated using the given (AE) Here, depicts the probability that picked random does then does interval dt and has calculated problem 1 Substitute P(t) and Substitute such that and the limits integration operate from 2mt (AE) Therefore the average loss to the per electron per Anonymous what the from the integral after substituting? Shouldn't be ???? Step The average energy dissipated per unit volume per unit be calculated by multiplying average energy (AE) with the electron density dividing the mean time between collsions that is Substitute Here, and highlights conductivity of the Therefore the average energy loss per centimetre per The power wire length and cross-section area Substitute E' Multiply divide the right-hand side the above equation by and equate Current defined the product of the current density and the area 4 therefore equate Substitute Therefore the power dissipated along the length with cross section area is