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Dielectrics

A vacuum-insulated parallel-plate capacitor with plate separation d  has capacitance C_0 . What is the capacitance if an insulator with dieletric constant \kappa and thickness d/2 is slipped between the electrodes without changing the plate separation?

Current and Ohm's Law

You've decided to protect your house by placing a 5.0 m tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is a good contact with the ground. From your research, you've learned that lightning bolts can carry up to 50 kA of current and last up to 50 \mu s .

a) How much charge is delivered for a lightning bold with these parameters?

b) You don't want the potential difference between the top and bottom of the lightning rod to exceed 100 V. What minimum diameter must the rod have?