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$\bullet$ $\bullet$ Three negative point charges liealong a line as shown in Figure 17.48 .Find the magnitude and direction of theFind the magnitude and direction of theelectric field this combination of chargesproduces at point $P$ , which lies 6.00 $\mathrm{cm}$from the $-2.00 \mu C$ charge measured perpendicular to the lineconnecting the three charges.

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Physics 102 Electricity and Magnetism

Chapter 17

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Cornell University

University of Sheffield

McMaster University

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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Three negative point charg…

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05:57

06:02

05:27

20:57

12:31

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Three point charges are ar…

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07:16

05:58

Three point charges are lo…

08:22

09:55

Three charges are arranged…

05:26

$\bullet$$\bullet$ Two poi…

before we start calculating electric fields, let's make sure we understand the situation. There are three charges. Q. One Q to thankyou three located along this line, and the distance between each of the charges is eight centimeters now. To the side, there is a point P which were interested in calculating the total electric field at and the distance prank you three MPs tens of years. And that's the same askew MVP. And in this angle here is 53.1 on both sides and the distance between que Tu and P s 67 years. Now you write the force diagram appoint P. You have an electric field, even one due to charge one pointing this way since you won his native Q three is negative, too. So there's the three pointing this way now. I broke these down into the microphone inside. Even. Why e three. Why? And that's the left Here. I have E, too. You want tax and the three x these air. Three additional electric field vectors. They're pointing to this left that didn't want draw three separate areas for so I've indicated by one arrow. So now let's use the formula that is equal to K magnitude of Q over R squared, where ours the distance between the charges in the location And so by symmetry, we know that the matter that you want any three appointee are the same and playing in the values here. For those we get 8.99 times 10 to the ninth. Best risque. Now Q is five times 10 to the minus six that's given to the problem and in the distance is just 0.1 meters square. And so this gives 4.49 times 10 to the six news per column. Now he, too, is going to be found in a similar way here. Ah, really similar. In fact, the only thing that changes is the queue. Here. We're going to use Q two of their charge, and we'll use the distance between Point P and Q two here, but same exact formula and same exact process. And I get 4.99 times 10 to the sixth Nunes for cool now in total. You, why is equal to even why plus e to y plus the three y? But since charged two is located horizontally to our point P the white component here of E to zero. And if we go back to our previous picture, you won. Why, Andy three. Why point in opposite directions and they're of equal magnitude. And so this one a big zero. Because if you won, why have some value e three? Why will be negative, that value and so little cancel Now e x The sum of the contributions and the extraction is equal to Yvonne X plus e to X plus the three X In this case, eat to excess, not zero. But you won't. Actually three X are still the same. But in this case, they don't cancel since they point the same direction. Instead they combine. And so e tu, In this case, I'm Ryan eat to excess. He too, since there was no e to why he too exited entirely too. Plus two times even one. And I'm gonna isolate the x component our writing co sign a 53.1 degrees. So this, too, comes from the fact that even X and the three X's are the same. So I combined them in the one and put it to outfront. And then the coastline is isolating the ex component. And then the one is just in reference to the large magnitude. Eveyone here. Now we can plug in everything that we know here. We don't need to. We know what you want. And so we find that E X is 1.4 times 10 to the seventh meters per Coolum. And so since e Y zero the totally is this and it points to the left and so that

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