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(1) Figure 26 shows five closed surfaces that surround various charges in a plane, as indicated. Determine the electric flux through each surface, $S_{1}, S_{2}, S_{3}, S_{4},$ and $S_{5}$ . The surfaces are flat "pillbox" surfaces that extend only slightly above and below the plane in which the charges lie.

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For $S_{1} : Q_{e n c l}=Q-3 Q=-2 Q \rightarrow \Phi_{E}=\frac{-2 Q}{\epsilon_{0}}$For $S_{2} : Q_{\text {encl}}=Q+2 Q-3 Q=0 \rightarrow \Phi_{E}=\frac{0}{\epsilon_{0}}=0$For $S_{3} : Q_{\text { end }}=2 Q-3 Q=-Q \rightarrow \Phi_{E}=\frac{-Q}{\epsilon_{0}}$For $S_{4} : Q_{\text {end}}=0 \rightarrow \Phi_{E}=\frac{0}{\epsilon_{0}}=0$For $S_{5} : Q_{\text {end}}=2 Q \rightarrow \Phi_{E}=\frac{2 Q}{\epsilon_{0}}$

Physics 102 Electricity and Magnetism

Chapter 22

Gauss's Law

Electric Charge and Electric Field

Electric Potential

University of Washington

Simon Fraser University

University of Winnipeg

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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(1) Figure 26 shows five c…

01:55

(I) Figure $22-26$ shows f…

02:47

Four closed surfaces, $S_{…

03:31

Figure 17.59 shows cross s…

03:40

01:03

A Gaussian surface for the…

05:31

(III) Uniform plane of cha…

01:11

Three point charges are lo…

So we are given a diagram that looks like this and we want to find the flux each of these surfaces as 1 to 5. They simply use the casian gases formula that flux is charged and closed, divided by ecelo naught so for surface s. 1 flux is equal to charge enclosed so the surface s 1 encloses whether this is q, 2 q, and this is minus 3 q surface s, 1 encloses q and minus 3, making the minus 2 so that minus 2 cube by exilo naught. Similarly, fi 2 is equal to. We have the surface 2, which covers all the 3 charges, so that's q plus 2 q, minus 3 q divided by exilonnaught, which is 0 surface 3, encloses simply the charges, 2 q and minus 3 q giving us 2 q minus 3 q epsilon naught, which is Minus q, by epsilon circus 4 encloses no charges whatsoever, which means the flux must be 0. Surface 5 includes only the charge 2 cube, which means the fluxes 2 cube siloa, that is it.

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