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0 Area A Area A, Area A, Area A2 igure 2 Figure 3 Figure 4

Part a Two large flat plates are separated by a distance d. The plates are connected to a battery. The surface area of the face of each plate is Ai, as shown in Figure 2. derive an expression for the capacitance in terms of Ai and d Part b A new capacitor is formed by attaching two uncharged metal plates, each with area A2, to the capacitor as shown in Figure 3. The battery remains connected i. When the new plates are attached, does the electric potential difference between the plates increase, decrease, or remain the same? Explain. ii. Write an expression for the work done by the electric field on a charge +go as it travels from the left plate of the caacitor to the right, Express vour auswer in terms of the given variables Explai

iii. 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 iv. Write an expression for the charge density on the plates of the capacitor. Is the charge density greater than, v. Write an expression for the total charge on one of the plates of the capacitor. Is this total charge greater than, vi. Use the definition of capacitance to find the capacitance of the enlarged pair of plates. Has the capacitance before the new plates were attached? Explain. less than, or equal to the charge density on the plates before the new plates were attached? Explain less than, or equal to the total charge on one of the original plates? Explain. increased, decreased or remained the same? Explain. art c Two plates with area Ai are held a distance d apart and are charged with a battery, as shown in Figure 2. The battery is then disconnected so the plates are uniformly charged with net charges +Q1 and -Q1, respectively Assume that all the charge is uniformly distributed on the inner surfaces of the plates. Two initially uncharged metal plates of surface area A2 are then attached to the original plates as shown in Figure 4. i. Find the final charge density on the plates. Did attaching the uncharged plates increase or decrease the charge density? Explain. ii. Find the electric potential difference between the plates. Explain iii. Calculate the capacitance of the enlarged plates. (Hint: The dimensions of the capacitors in parts b and c are the same

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