4. The Parallel-Plate Capacitor with Fixed Potential Two large flat metal plates are separated by a distance d. The plates are connected to a battery as shown below. The surface area of the face of each plate is A1. V a. Write an expression for the capacitance in terms of Aj and d. Explain how you found it. b. A new capacitor is formed by attaching two uncharged metal plates, each with area A2, to the capacitor as shown. The battery remains connected. Area A Area A,i. When the new plates are attached, does the electric potential difference between the plates increase, decrease, or remain the same? Explain your conclusion. ii. Write an expression for the work done by the electric field on a charge +q. as it travels from the left plate of the capacitor to the right. Express your answer in terms of the given variables. Explain. ili. Write an expression for the magnitude and direction of the electric field between the plates. Is the magnitude of the electric field greater than, less than, or equal to the magnitude of the electric field between the plates before the new plates were attached? iv. Write an expression for the charge density on the plates of the capacitor. Is the charge density greater than, less than, or equal to the charge density on the plates before the new plates were attached? Explain. v. Write an expression for the total charge on one of the plates of the capacitor. Is this total charge greater than, less than, or equal to the total charge on one of the original plates? Explain. vi. Use the definition of capacitance to determine the capacitance of the enlarged pair of plates. Has the capacitance increased, decreased, or remained the same? Explain how you can tell