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184_notes:examples:week7_charging_capacitor [2017/10/06 18:29] – [Solution] tallpaul | 184_notes:examples:week7_charging_capacitor [2017/10/06 18:34] – [Solution] tallpaul | ||
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- | Notice that we also used the charge of the capacitor in our argument for why the current drops off like it does. We basically argue that the charge graph will look like a flipped current graph: rapidly accumulating charge at first, and gradually slowing down in accumulation until equilibrium (" | + | Notice that we also used the charge of the capacitor in our argument for why the current drops off like it does. We basically argue that the charge graph will look like a flipped current graph: rapidly accumulating charge at first, and gradually slowing down in accumulation until equilibrium (" |
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Lastly, we wish to produce a graph of the potential difference between the plates. We can pull from a previous in-class project in which we found the electric field from a large plate of charge. It is pretty much constant, and depends on the charge of the plate like so: | Lastly, we wish to produce a graph of the potential difference between the plates. We can pull from a previous in-class project in which we found the electric field from a large plate of charge. It is pretty much constant, and depends on the charge of the plate like so: | ||
$$E_{plate} = \frac{Q_{plate}}{2\epsilon_0 A_{plate}}$$ | $$E_{plate} = \frac{Q_{plate}}{2\epsilon_0 A_{plate}}$$ | ||
+ | Notice that we do not necessarily need to remember this equation -- the electric field of everything we have looked at so far depends linearly on the charge. | ||
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We also remember that potential difference across a constant electric field is just the electric field times the distance. Since the distance between the plates is unchanging and the electric field simply scales with $Q$, we can expect the voltage graph to have the same shape as the charge graph: | We also remember that potential difference across a constant electric field is just the electric field times the distance. Since the distance between the plates is unchanging and the electric field simply scales with $Q$, we can expect the voltage graph to have the same shape as the charge graph: | ||