Discharging current in capacitor
A parallel-plate capacitor with circular plates of radius R is being discharged. The displacement current through a central circular area, parallel to the plates and with radius R/2, is 2.0 A. What is the discharging current?
Answer
This problem is easiest if you solve in terms of variables and plug in the 2.0 A at the very end. Start with the expression for the displacement current. Can you write the electric flux as the field E times an area? You also know the expression for a parallel plate capacitor. What is E inside? Remember that the discharging current I = dQ/dt, where Q is the charge on the capacitor.
This should be enough to solve the problem, but you have to be careful when you write down areas: there are two different areas involved -- the entire plate area and the center circular area.
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This problem is easiest if you solve in terms of variables and plug in the 2.0 A at the very end. Start with the expression for the displacement current. Can you write the electric flux as the field E times an area? You also know the expression for a parallel plate capacitor. What is E inside? Remember that the discharging current I = dQ/dt, where Q is the charge on the capacitor.
This should be enough to solve the problem, but you have to be careful when you write down areas: there are two different areas involved -- the entire plate area and the center circular area.