Announcements

1. Announcements

2. I + + + - - - Current • Current, I, is the rate of flow of electric charge, dQ/dt is the instantaneous current • It is measured in Coulombs/Second • Unit is Ampere (amp, or A) • The direction of current is the direction that positive charges would flow • Or the opposite of the direction that negative charges flow • There must be a net transport of charge to have a current.

3. - - - Quiz • Suppose we have a current from a flow of electrons to the right. • In what direction is the current? • In what direction is the electric field? • To the right • To the left • Up • Down • None of the above

4. Quiz • Suppose we have a current from a flow of Calcium (+2) ions • In what direction is the current? • In what direction is the electric field? • To the right • To the left • Up • Down • None of the above +2 +2 +2

5. Current Density • Current Density, J, is the amount of current flow through a unit area • Assuming uniform current parallel to dA • Note: For a fixed area, the current density is independent of shape • Remember: Current has a direction! Area A Current I

6. Current: Details • When thinking about current flow, think about fluid flow. • Remember that a conductor at equilibrium has no field inside • For there to be a current one cannot be at equilibrium • There has to be a potential difference, otherwise for every carrier moving in one direction another one is moving in the opposite • Think about fluid flow: there has to be a potential difference for fluid to flow otherwise water is stagnate. Area A Current I

7. Current I Current: Flow • When thinking about current flow, think about fluid flow. • The flow in equals the flow out • So the current in equals the current out I3 I2 I1 Area A I1= I2+ I3

8. Quiz • In which of the following situations is the magnitude of the current the largest 3C/s 2C/s 6C/s 7C/s + + + + 5C/s 1C/s 5C/s - - - A C D B Area A Current I

9. Microscopic Description of Current: Qualitative • Microscopically current is due to the movement of charge carriers • In the Drude model, the electrons diffuse in the absence of • an applied field • Electron Gas When a field is applied, the symmetry of the “motion” of the electrons is broken and there is a net drift.

10. Microscopic Description of Current: Math • Assume uniform motion and density of charge carriers • The charge in a wire of length L can be calculated q=(nAL)e, for electrons • The total charge moves through a cross-section in: t=L/v ; v is the drift velocity A L

11. Microscopic Description of Current: Math • Assume uniform motion and density of charge carriers • I=q/t=nALev/L =nAev • This implies (J=I/A) that J=(ne)v ne is the charge carrier density A L

12. Quiz • Suppose I have an ion channel through which sodium (+1) ions flow • Suppose I have another ion channel through which calcium (+2) ions flow. If the concentration of the ions are the same, and drift velocities are the same, then how are the current densities in thetwo channels related? • The current densities are identical • The current density in the sodium channel is twice the current • density in the calcium channel. • C) The current density in the calcium channel is twice the current • density in the sodium channel. • D) The current density in the calcium channel is four time the current density in the sodium channel.

13. Conductivity • In an ideal material (superconductor) no force is needed to keep the charge moving • In most materials, electric field is required to make the current move • the current is proportional to the electric field, and the conductivity • The conductivity is a property of the material Electric Field E Current I

14. Conductivity • In most materials, electric field is required to make the current move • the current is proportional to the electric field, and the conductivity Empirically, • The conductivity is a property of the material • the resistivity is the reciprocal of the conductivity, nothing more!