Show that the average energy of an electron in a one-dimensional metal is related to the Fermi energy by \(\bar{E}=\frac{1}{2} E_{\mathrm{F}}\).

Text Transcription:

bar E=1/2 E_F

Chapter 21: electric current & DC - circuits Overview: Charges in motion - Mechanical motion - Electric current How charges move in a conductor Definition of electric current ● Charges in motion Up to now we have considered - Fixed charges on isolated bodies - Motion under simple forces (e.g. a single charge moving in a constant electric field) We have also considered conductor - Charge are free to move - We also said that E=0 inside a conductor If E=0. and there is any friction present. No charges will move. Create electric field inside , so that charge will move. Make electric potential at both end of the conductor. ● Charges in motion We know from experience that charges do move inside conductors - this is the definition of a conductor Is there a contradiction No Up to now we have considered isolated conductors in equilibrium - Charge has nowhere to go except shift around on the body - Charges shift until they cancel the E field, then come to rest. Now we consider circuits in which charges can circulate if driven by a force such as a battery. ● Analogy with fluids Consider a hose filled with water: - Need a difference of potential for fluid to flow - Same is true for electric charges Need to have one electric potential higher than another. ● Current definition ▯ Consider charges moving down a conduction in which there is an electric field. If we take a cross , over some amount of time Δt we will count a certain number of charges (or total amount of charge) ΔQ