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(II) A solid metal sphere of radius 3.00 $\mathrm{m}$ carries a total charge of $-5.50 \mu \mathrm{C}$ . What is the magnitude of the electric field at a distance from the sphere's center of $(a) 0.250 \mathrm{m}$ , (b) $2.90 \mathrm{m},(c) 3.10 \mathrm{m},$ and $(d)$ 8.00 $\mathrm{m}$ ? How would the answers differ if the sphere were $(e)$ a thin shell, or $(f)$ a solid nonconductor uniformly charged throughout?

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a) $r=0.250 m$b) $r=2.9 \mathrm{m}$c) 5140$N / C$d) 772$N / C$e) since the charges tend to be on the surface of the metal, so the would be no different for a thin metal shell.f) $458 \mathrm{N} / \mathrm{C}$5310$N / C$5140$N / C$772$N / C$

Physics 102 Electricity and Magnetism

Chapter 22

Gauss's Law

Electric Charge and Electric Field

Electric Potential

Brandon C.

April 28, 2021

wait wait for part c. wait happened to the epsilon ( 8.85x 10^-12 ) what happened to pi what happened to the 4. like

Cornell University

Hope College

University of Winnipeg

Lectures

13:02

In physics, potential energy is the energy possessed by a body or a system due to its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units (SI) is the joule (J). One joule is the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre). The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concepts of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body, and not on the specific path between them. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy.

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

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(II) A solid metal sphere …

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So we have a solid metal sphere which has a charge off minus 5.5 micro forums. We want to find the electric field very a different set of distances, first being to the 12250 meters. Now let's look at this case first because this is a metal disappear. All of its charge will be reciting from the surface on because it's a medal. The field inside would be zero and inside for any distance less than three meters from the center. The field will be zero in this whole region. So Sarah, I want to 1st 0 meters is inside the sphere and helps Elephant field will be zero Barbie. We're looking at 2.90 meters, which is somewhere here, which is still within the spear on. Hence, the electric field is zero, but for boxy, the distance is 3.1 meters just outside this fear. Now there is another thing to note spectacle. Charge distributions act as if the whole charge was concentrated at the center for objects outside the spear. It is this. At this point it will be as if the whole charge of minus 5.5 micro problem was concentrated at the center. Hence the electric field. Well, basically, Q Bye. Four by our square. Excellent. Not just like a point charge, but notice that we're simply finding the magnitude of charge. The direction will simply be radial. It is in this direction towards the center of the spear. So the magnitude will be charged. Gonna be five point fire into 10 Part six hoodlums. One sec. There is another fight here for about pie now one by four. By excellent, not has value off. 8.9 80 into 10. Part nine Newton Meters Square Park A landscape Gotham Square, if you remember, provided by our square is 3.1 meter square. Excuses 5140. I noticed the units. It was a cool appear meter squared on the unit's um you didn't call him. As for Littlefield, similarly for body, we're looking at a distance. Ain't me just so again. It says if we have ah, charge off minus 5.5 micro columns on it. Eight meters distance. We're finding the electric field so the electric field is again simply you by four. By accident. Not ask there the charges again. 5.510 4 minus six for by one by four place Alana has value off 8.98 into 10 9 New Times Square for cooling squares divided by eight meter squid discusses 7 72 New Temple Coolum In fact, you could not. You need not have done this. I know that. You know this is 5140 it 3.4 meters. You know that here we divided by 3.1 square for to get the feel it eight meters will have really wide instead by eight square. So you could simply multiply this by three points one by eight all square, and you'll have the same answer now for Bar E. We wantto consider what happens if this if it was a tin metal shell instead. The answer is nothing else. Nothing different. Even if it wasn't in my job, it's very good to shell. The child would still be on the upside and the child the field inside of still zero and hence the all the values would be the same. But the next part is a little interesting. What would happen if this fear had constant Chaz density. Something like a dialectic on which the heart has been put into for this problem. Obviously, For any point outside the spear, it is still the same. Hey, start obvious by the way it has. You need to use costs, right to figure out that for anyone outside the sphere, the field will be as if the whole charge that the center of the spear. But for points inside the sphere, we have a formula that looks like this on before were excellent. Not Cuba are not. You are we are not. Is the radius off the sphere on R is the distance at which we're finding the This is very easy toe Dr. Actually, let's say this is our mark. The tibia finding it just, uh, we would consider a Gaussian surface a spectacle. Gaussian surface The tires that is outside the spear will not effect the feeling point are so only the child that is inside the spear would affect it. So if let's say the total charged density would be you by four by three pi r cubed because the art market, because the charges uniformly distributed. So on this Gaussian surface we can see that the flux will be electric field times area and the area will be four by our square. But this is equal to Cuba. Excellent. Not where he used the n close shot. The enclosed charge would be road signs. The enclosed volume, which is or by three by are cute be righted. Bite, I said I'm not now. We simply cancel before five on. We haven't out here. This gives us easy will do so by three years along now, using the formula for probably help We have really took you by or by fi Fi are not cute into three years alone, Not into far I'm sorry for about this are here. Is that our You can see that this is for seeing as this formula that's it. So for the parts cnd, the field will be the same. But for parts A and B, it would be different for Bar Dave, where we had to find the field distance thereupon to five meters. We'll use the formula electric field as cell was one by four. By exit or not, Cuba are not cube into our So that is we know the farm before, based on artist a 0.988 in 10 9 Hugh is 5.5 10 pound minus six, but are not, as you know is three meters. So are not your mystery. Cute things are is thereupon to fight. This gives us 4.458 you're cool on. Similarly, for distance 4.9 meters, we use the same formula given this one before the accident out of 8.9 aye, dating to 10.9. Q is 51 $500 minus six by three Cube on for the distance is tau nine, instead giving us 5310 Newton couldn't be other two distances. Three people, one meters and 80 just will be the same, that's it.

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