Question

1. We know that the electric field within a conductor at equilibrium must be zero. a) We thought about that in the context of neutral conductors, in which the number of electrons and protons balance out. But would it remain true that $$E = 0$$ even if you put some extra charge on the conductor? Explain briefly. Spoiler alert: the answer to part a is yes. This means that the extra charge must rearrange itself in just the right way to produce $$E = 0$$ within the conductor (though not outside). If the conductor is not symmetric, this is a rather complex problem to solve, and yet the charges just "know" where to go. b) There is something that we can know about the location of these extra charges even without a complicated calculation, however. Thinking about Gauss's Law, describe the only possible region of the conductor where the extra charge could be located. c) Does your reasoning for part (b) require the conductor to be a symmetric shape such as a sphere?

          1. We know that the electric field within a conductor at equilibrium must be zero.
a) We thought about that in the context of neutral conductors, in which the number of electrons and protons balance out. But would it remain true that $$E = 0$$ even if you put some extra charge on the conductor? Explain briefly.

Spoiler alert: the answer to part a is yes. This means that the extra charge must rearrange itself in just the right way to produce $$E = 0$$ within the conductor (though not outside). If the conductor is not symmetric, this is a rather complex problem to solve, and yet the charges just "know" where to go.

b) There is something that we can know about the location of these extra charges even without a complicated calculation, however. Thinking about Gauss's Law, describe the only possible region of the conductor where the extra charge could be located.

c) Does your reasoning for part (b) require the conductor to be a symmetric shape such as a sphere?

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1 we know that the electric field within a conductor at equilibrium must be zero a we thought about that in the context of neutral conductors in which the number of electrons and protons bal 57038

Added by Vanesa G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Gregory Devenport

02/06/2023

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The question asks if the electric field ($$E$$) within a conductor at equilibrium remains zero even if extra charge is added to the conductor. Show more…

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1. We know that the electric field within a conductor at equilibrium must be zero. a) We thought about that in the context of neutral conductors, in which the number of electrons and protons balance out. But would it remain true that $$E = 0$$ even if you put some extra charge on the conductor? Explain briefly. Spoiler alert: the answer to part a is yes. This means that the extra charge must rearrange itself in just the right way to produce $$E = 0$$ within the conductor (though not outside). If the conductor is not symmetric, this is a rather complex problem to solve, and yet the charges just "know" where to go. b) There is something that we can know about the location of these extra charges even without a complicated calculation, however. Thinking about Gauss's Law, describe the only possible region of the conductor where the extra charge could be located. c) Does your reasoning for part (b) require the conductor to be a symmetric shape such as a sphere?

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Transcript

00:01 Okay, we're investigating gauss's law here.

00:05 We're using gauss ' law to think about where the excess charge and a conductor goes.

00:10 So let's draw our conductor here.

00:16 And we're told that it gets negatively charged, right? let's see.

00:29 Yeah, negative charge.

00:30 Okay.

00:31 So where does the charge go if it's free to move around? and something they tell us here is that the electric field in a conductor is zero everywhere inside the conductor.

00:47 So that's an important thing to know.

00:51 So question one, we want to think about what is the amount of excess charge enclosed by the dashed surface just below the surface of the conductor.

01:08 So how much charge is contained by this black dashed line we've drawn? and we want to use the fact that electric field equals zero.

01:17 Let's use gauss's law, right? the closed surface integral of e .da equals q enclosed and closed over epsilon nut.

01:40 So if we know that the electric field equals zero, that makes this entire left -hand side equals zero, right? q enclosed or epsilon not.

01:54 We know for a fact that epsilon not is not equal to zero.

01:58 That's just a constant.

01:59 So for this equation to be true, the enclosed charge has to equal zero...

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