Exam2_2010Spr_Solutions - MASSACHUSETTS INSTITUTE OF...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2010 8.02 Exam Two Spring 2010 Solutions Question 1: (5 points) Circle the correct answer. Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and are separated by a distance d. The capacitor is connected to a battery. Suppose the plates are pushed together until they are separated by a distance D = d/2. How does the final electrostatic energy stored in the capacitor compare to the initial energy? a) Final is half the initial. b) Final is one fourth the initial. c) Final is twice than initial. d) Final is four times the initial. e) They are the same. Answer c. Because the capacitor is connected to the battery, the potential difference across the plates is constant. Therefore the ratio of the final stored energy to the initial stored energy is proportional ratio of the final capacitance to the initial capacitance, 2 2 1 1 / / / 2 2 f i f C i C f i U U C V C V C C = Δ Δ = . For a parallel plate capacitor, the capacitance is inversely proportional to the distance separating the plates, 0 0 ( / ) A Q Q A C V Ed d d ε σ σ ε = = = = Δ . Therefore the ratio of the capacitance is / / /( / 2) 2 f i i f C C d d d d = = = . So / 2 f i U U = .
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