Question

7. A large, charge-neutral metal sheet of thickness b is placed between, and parallel to, the plates of a parallel plate capacitor. The separation between the plates is d and the area of each is A. The dimensions of the sheet and the capacitor plates can be regarded as much larger than the separation between them. The capacitor has been charged and disconnected from the source prior to inserting the sheet. (a) How does the electric field between each plate and the sheet compare to the electric field between the two original capacitor plates, when the sheet was not present? What is the electric field within the sheet? (b) In terms of A, d, and b, what is the new capacitance, with the sheet between the plates? Does it matter where the sheet is placed between the plates? Explain. (c) Work out an expression for the fraction of the new capacitance, C, to the old capacitance, C0, depending on d and b, and calculate it for the situation that b=d/2. Explain your answer. (d) For b=d/2, what is the fraction U/U0 of the electrical energy stored in the new capacitor relative to the old one?

          7. A large, charge-neutral metal sheet of thickness b is placed between, and parallel to, the plates of a parallel plate capacitor. The separation between the plates is d and the area of each is A. The dimensions of the sheet and the capacitor plates can be regarded as much larger than the separation between them. The capacitor has been charged and disconnected from the source prior to inserting the sheet. (a) How does the electric field between each plate and the sheet compare to the electric field between the two original capacitor plates, when the sheet was not present? What is the electric field within the sheet? (b) In terms of A, d, and b, what is the new capacitance, with the sheet between the plates? Does it matter where the sheet is placed between the plates? Explain. (c) Work out an expression for the fraction of the new capacitance, C, to the old capacitance, C0, depending on d and b, and calculate it for the situation that b=d/2. Explain your answer. (d) For b=d/2, what is the fraction U/U0 of the electrical energy stored in the new capacitor relative to the old one?

$7. A large, charge-neutral metal sheet of thickness b is placed between, and parallel to, the plates of a parallel plate capacitor. The separation between the plates is d and the area of each is A. The dimensions of the sheet and the capacitor plates can be regarded as much larger than the separation between them. The capacitor has been charged and disconnected from the source prior to inserting the sheet. (a) How does the electric field between each plate and the sheet compare to the electric field between the two original capacitor plates, when the sheet was not present? What is the electric field within the sheet? (b) In terms of A, d, and b, what is the new capacitance, with the sheet between the plates? Does it matter where the sheet is placed between the plates? Explain. (c) Work out an expression for the fraction of the new capacitance, C, to the old capacitance, C0, depending on d and b, and calculate it for the situation that b=d/2. Explain your answer. (d) For b=d/2, what is the fraction U/U0 of the electrical energy stored in the new capacitor relative to the old one?$

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