Question

In the lecture about Displacement Currents, (first 15 minutes) he says that electric field only exists between the plates of the capacitor. The wire connected to the capacitor has current on it; isn't there an electric field inside of the wire?

Answer 1

The wire's radius is very small compared to the capacitor and he just tosses out the consideration of the electric field in the wire because he wants to illustrate the importance of adding the displacement current term to Amperes law with Maxwell's equation. Further into the lecture he draws a graph of the electric field as it changes relative to radius away from the center of the plain disk plates. So for consideration of that problem the electric field does actually exist in the wire its just that since the diameter is so small compared to the capacitor plates you can ignore it.