Dielectrics: Steve has been with his partner for 4 years. Every year on the day that they met, he plans a romantic dinner. However, this year, Steve is stuck in the lab testing equipment for his physics students. To make up for being late, he decides to make for his partner a capacitor necklace such that the capacitor charge gives the date that they met: Q = 8.15 nC (August 15).

(a) Making a stylistic choice, Steve decides to go with 1 cm² for the area A of the plates. Using the only battery he has access to (50 V), what separation d must Steve maintain between the plates to get the desired charge Q? Assume the plates are perfect conductors. What is the capacitance?

(b) Steve decides that the separation is a bit too thin to constitute a stable configuration. Though since he took physics himself, he knows that he can have a larger separation distance if he adds a dielectric in between the plates. What dielectric constant must he use to achieve a separation of 5 mm?