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Problem 3 Let's say we have two infinitely large parallel plates a distance d apart. The plates are hooked up to a battery that maintains a certain potential difference, V. We know that the charge on each capacitor plate is σ and -o.There is currently no dielectric between the plates. a) Using Gauss's law, what is the E field in the center of the capacitor? Is there E field outside of the capacitor? Is the E field uniform within the capacitor? Explain your reasoning for each. b) Using the E field from part (a), calculate the potential drop across the capacitor plates. c) We maintain the same potential difference that we solved for in part (b), but we slide in a dielectric with dielectric constant K. K can also be described as e/o. How much charge can be stored? How does it compare with the old charge? What is the intuition behind € and K? d) Say that each plate only has an area A and we ignore fringing fields. Because capacitance is defined as C = Q/V, what is the expression for capacitance using quantities we solved for in parts c and b?

Problem 3 Let's say we have two infinitely large parallel plates a distance d apart. The plates are hooked up to a battery that maintains a certain potential difference, V. We know that the charge on each capacitor plate is σ and -o.There is currently no dielectric between the plates. a) Using Gauss's law, what is the E field in the center of the capacitor? Is there E field outside of the capacitor? Is the E field uniform within the capacitor? Explain your reasoning for each. b) Using the E field from part (a), calculate the potential drop across the capacitor plates. c) We maintain the same potential difference that we solved for in part (b), but we slide in a dielectric with dielectric constant K. K can also be described as e/o. How much charge can be stored? How does it compare with the old charge? What is the intuition behind € and K? d) Say that each plate only has an area A and we ignore fringing fields. Because capacitance is defined as C = Q/V, what is the expression for capacitance using quantities we solved for in parts c and b?

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Problem 3 Let's say we have two infinitely large parallel plates a distance d apart. The plates are hooked up to a battery that maintains a certain potential difference, V. We know that the charge on each capacitor plate is o and -o.There is currently no dielectric between the plates. a) Using Gauss's law, what is the E field in the center of the capacitor? Is there E field outside of the capacitor? Is the E field uniform within the capacitor? Explain your reasoning for each. b) Using the E field from part (a), calculate the potential drop across the capacitor plates. c) We maintain the same potential difference that we solved for in part (b), but we slide in a dielectric with dielectric constant . K can also be described as e/o. How much charge can be stored? How does it compare with the old charge? What is the intuition behind € and ? d) Say that each plate only has an area A and we ignore fringing fields. Because capacitance is defined as C = Q/V, what is the expression for capacitance using quantities we solved for in parts c and b?
Transcribed Image Text:Problem 3 Let's say we have two infinitely large parallel plates a distance d apart. The plates are hooked up to a battery that maintains a certain potential difference, V. We know that the charge on each capacitor plate is o and -o.There is currently no dielectric between the plates. a) Using Gauss's law, what is the E field in the center of the capacitor? Is there E field outside of the capacitor? Is the E field uniform within the capacitor? Explain your reasoning for each. b) Using the E field from part (a), calculate the potential drop across the capacitor plates. c) We maintain the same potential difference that we solved for in part (b), but we slide in a dielectric with dielectric constant . K can also be described as e/o. How much charge can be stored? How does it compare with the old charge? What is the intuition behind € and ? d) Say that each plate only has an area A and we ignore fringing fields. Because capacitance is defined as C = Q/V, what is the expression for capacitance using quantities we solved for in parts c and b?
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