The circular plates of a parallel-plate capacitor have a radius of \(30 \mathrm{~mm}\). A steady 2.0 -A current is charging the initially uncharged capacitor, and the surface charge on the plates is distributed uniformly.

(a) Derive an expression for the magnitude of the electric field between the plates as a function of time.

(b) In Figure P30.29a, the flat circular surface between the capacitor plates has a radius of \(10 \mathrm{~mm}\). What is the displacement current through this flat circular surface?

(c) Consider the open surface shown in Figure P30.29b, a cylindrical shell open at the right end that passes through the left capacitor plate. If the radius of the flat circular end is \(10 \mathrm{~mm}\), what is the displacement current through the open shell?

(d) Why is your answer to part \(c\) different from your answer to part \(b\) ? Why are both these answers different from \(I=2.0 \mathrm{~A}\), the current through the capacitor?

Data from Figure P30.29

(a) (b) T 000 #0 T