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Problem 40 Hard Difficulty

The dome of a Van de Graaff generator receives a charge of $2.0 \times 10^{-4}$ C. Find the strength of the electric field (a) inside the dome, (b) at the surface of the dome, assuming it has a radius of $1.0 \mathrm{m},$ and $(\mathrm{c}) 4.0 \mathrm{m}$ from the center of the dome. Hint: Sce Section 15.5 to revicw propertics of conductors in electrostatic equilibrium. Also, note that the points on the sur-
face are outside a spherically symmetric charge distribution; the total charge may be considered to be located at the center of the sphere.

Answer

a. (a) The dome is a closed surface. There are no electric field lines inside the dome. So, the strength of the electric field inside the dome is zero.
b. $1.8 \times 10^{6} \mathrm{N} / \mathrm{C}$
c. $1 \times 10^{5} \mathrm{N} / \mathrm{C}$

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Video Transcript

Heather students, let's start or discussion. Ah Vendor Graaff generator render Graaff generator Uh, I suppose this is the dorm off our Pendergraph janitor. Okay? No, we have to find out the electric field at various places off this one. The graph generate Firstly, we have to find out the electric field on a point that lies inside this Wedneday Craft 100 inside this dome. Okay, so basically electric field at point B. That is inside. Well oh, basically the potential at point p that lies inside will be one upon four by up silent Nord you by where r is the radius off this dorm and use the total charge that lies on the surface off the dome. This is the cue, Okay? No, you're imagine you're wondering that. Why I am saying the potential inside by taking the disco charge basically by the vendor Graaff generator, properties and principal the potential lies at the surface is exactly equal to potential Lies at the insight. Okay, So VP inside is fun upon for Perhaps I'll knock you by our so electric Philby will also re by our That is so. It will be one upon four by absolute note Que by a square. Okay, so my soul doing this If the value off charge Louis to entertain this par minus four problem and the Radius author dorm is born meter. So by putting the values nine into tennis Part nine in tow to entertain this far minus for by one square, we will get an answer off 1.8 and through time This part six Newton Pakula see at point realize inside. So this electric field is exactly similar on the surface. So at point B dash, which lies on the surface of the dorm, electric field is equal toe 1.8 into 10 days by six. New TEMPER COLUMN as because the potential at the surface and the inside are exactly equal. So the electric field at saw phase and insight is exactly equal. Okay, so this is that point a dash which lies on the surface now support. We have to find out electric field on another point, that life outside this door, let's name them pay double dish and the separation between ST trend pain Doubles Laissus four meter. No, we have to find out electrified so basically potential at p dish. The backlash will be one upon for by absolute Nord through by our and the electric feel. At this point, people, at this point of it'll be one upon four by up silent north you buy are square. So nine into 10 this by nine in tow, Toe into 10 This part minus four by four meters square. So we will get the answer off. 4.5 in tow. Dan Dis par five, New Temple Coolum. Okay, this is the electric field at outside off. Odo. Well, this is all for me for this radio. I hope you will like the video. Thank you.

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Top Physics 102 Electricity and Magnetism Educators
Elyse G.

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