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# A nonconducting, thin plane sheet of charge carries a uniform charge per unit area of 5.20$\mu \mathrm{C} / \mathrm{m}^{2}$ as in Figure 15.30 . (a) Find the electric field at a distance of 8.70 $\mathrm{cm}$ from the plate. (b) Explain whether your result changes as the distance from the sheet is varied.

## a. Therefore, the magnitude of the electric field at all distances greater than zero from the plane is $2,94 \times 10^{5} \mathrm{N} / \mathrm{C}$ .b. The electric field does not alter with distance as long as the distance is small compared with the dimensions of the sheet.

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### Video Transcript

Okay, So for this question, where else to consider a flat uniforms sheet of charge? Andi is also said to be thin, so and rushed to find the field a certain distance away from it. So what we wanted to realize, first of all, is that because the dimensions of the sheet I'm much, much smaller in the distance. There is actually no dependence on distance in the Ethier, so it's gonna be the same, however far away we consider. Okay, So what we want toe realize first, is that this shape has a charge density of five point e times 10 to the minus six que items per meter square. And that's a charge density. Ah, Now we need Teoh realize a galaxy in relationship that will be the area of our gatting surface, Which is this here on this hit because this was parallel to the left of the sheet. I'm so has flux moving through it. So we do the area multiplied by the charge density on the sheet, and we know that's gonna be equal to the surface into girl of the D Field in this case, dots D A. Okay, so when we do this into group. And we need to realize the fact that if each of these areas were calling a and then actually there's two of the Serie introduce a factor of two into our equation. Give us two day, okay? And we actually in the e things rather than the field. And this is way you re allowing consideration. Teoh turned the permitted ity of free space on rather than the pure electric fields. So we need this identity here with a D food that equal to the e food he failed, multiplied by ab silent note for it could be depending on the medium through which the electrically moving that could be a different number. Okay. And so this is gonna leave us with area times a charge. Density is equal to see a upside on north pounds. A you can see here that are a They're gonna cancel. I asked me. Predicted there is no dependence in the distance. We just get a to be equal to charge. Density divided by time. Outside on north. Okay, on. So we put up here 5.6 times 10 the minus six, divided by two, multiplied by eight. That's gonna be there once. And then we need to state that unless we're considering very, very close up to the sheet where the distance is gonna be a a similar magnitude to the whip. And then actually, this e food is gonna be constant at where the distance we consider.

University of Sheffield