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A parallel-plate air capacitor is made from two plates 0.200 m square, spaced 0.800 $\mathrm{cm}$ apart. It is connected to a $120-\mathrm{V}$ battery. (a) What is the capacitance? (b) What is the charge on each plate? (c) What is the electric field between the plates? (d) What is the energy stored in the capacitor? (e) If the battery is disconnected and then the plates are pulled apart to a separation of $1.60 \mathrm{cm},$ what are the answers to parts (a), (b), $(c),$ and $(d) ?$

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Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 18

Electric Potential and Capacitanc

Kinetic Energy

Potential Energy

Energy Conservation

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

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This is a classic capacitor problem. We know that it's made from two plates that, um, have an area of 20.2 Oh, meters Looks funny. You fix that great. And then we want to get we know it's the distance is 0.8 centimeters. So d is equal to 0.0 a meters. And the battery it's connected to is 100 and 20 volts, and we want to get the capacitance so capacitance for that we want to use capacitance is equal to Absalon, not a over d. We could have used the voltage if we had known the charge. So I'm just gonna calculate Absalon la times this a divided by that d and see what I got Time was strange two divided by Plan H. And then I got 2.21 times 10 to the minus 10 fair ad and then be asks for the charge and each plate. So for B C is Q over B, so Q is equal to CV, so we just need to multiply be times that capacitance that we just calculated. So we want to take this whole thing and multiply it by 120. So I got two point 2.676 Sorry. 66 times. 10 to the minus C When I say seven or eight. So you 80.6 2.66 times 10 to the minus heat. Cool ums. And next we want to find probably the energy or something. Let's see electric field So electric field is bolted She bided by distance So 1 20 divided by 200.0, a beaters Playing that into a calculator I got 15,000 volts per meter and for D, the energy stored in the capacitor And now we have energy. So I think the fastest one is Q b. So I'll just do well because it isn't You don't have to score anything. This is not really that fast. Yeah, cause Q A CV? Yeah, CVS word. Okay, so I'm gonna plug in this charge times the voltage of this 266 number, and then times 120 times claimed by I got 1.59 times 10 to the minus six. Jules, not really. Right. So let me make sure. So he was 10 to the minus. A bee's gives you another babe to exponents, So I guess that passes that check. Okay. And then e if it were disconnected, and then you separated the plates toe 1.6 centimeters. So you doubled it. So we want to know how all the answer is changed. So a So this pope ages about D goes to D times two. And then we say it's always connected to this 120 volt battery. Oh, it's not. The battery is disconnected. Okay, well, the capacitance is still gonna be ours. The capacitance is inversely proportional to D. So cut. The capacitance is going to go to the original capacitance divided by two. So that's gonna be, um, 2.21 divided by two. So then that's gonna be one point 11 times 10 to the minus 10 fare ads. Okay, so that's a and then for B. We want to get the charge on each plate. That's going to stay the same. There's no transfer of charge, especially since the battery is disconnected. And, um, the electric field just depends on charge, so that will also be the same. And for d, the energy stored. So, um, let's use to you is 1/2 Q b this stays the same. And then oh, um, no. Let's not use this one. Forget that. Um, let's use the most direct one. So let's use the one with Q and see, So that's Q squared over. See? So see? Gets have been you against double. So you equals, um, twice the original value. So you is gonna be, um, two times 1.59 So let's see, That's basically 1.6. So that's gonna be three point 18 What? And then they explain it. 18. 18 s 30. You must use nine. 09 So 1.59 I'm trying to just do mental Matthew at 1.5 mine times 10 to the minus. Sechs, Jules. And for e. M. We want to know. Oh, that was it. Okay, great.

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