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(II) A cube of side $\ell$ is placed in a uniform field $E_{0}$ with edges parallel to the field lines $(a)$ What is the net flux through the cube? (b) What is the flux through each of its six faces?

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a) $\phi_{E}=0$b) $\phi_{\text {enter} \text {ing}}=-E \ell^{2}$$\phi_{\text {exiting}}=+E \ell^{2}$$\phi_{\text {others}}=0$

Physics 102 Electricity and Magnetism

Chapter 22

Gauss's Law

Electric Charge and Electric Field

Electric Potential

Cornell University

University of Michigan - Ann Arbor

University of Washington

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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(II) A cube of side $l$ is…

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(II) A cube of side 8.50 c…

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2 A cube Of side 8.50 cm i…

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(a) Find the electric flux…

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A cube whose sides are of …

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A cube of edge length $\el…

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(II) A point charge $Q$ is…

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The cube in Fig. $\mathrm{…

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What is the net flux of th…

Okay, so doing Chapter 22 problem three here. So it says a cube of side lynx l was placed in a uniform field electric field. He knocked with EJ is parallel to the field lines. Okay, so part ay says what is it? The net flux through cube. Okay, so if the field is uniform, no lines originate or terminate inside the cube. So if we think about this being our cue here, very, very poor, drawn, poorly drawn cube. Our electric field is coming in here. It's uniform across all space. So the electric field going through this area is the same going out. So that means we know that the electric flux must be zero because no lines originate or terminate inside the Cube. Awesome Part B. Barbie says. What is the flux through each of its six faces? Okay, so this was the net flux, right? But each face itself is going to have its own flux. There are two opposite faces with field lines perpendicular to the faces in the other four. Faces have lines parallel, so that means two of the faces are perpendicular through the field lines and four of them are parallel to the fuel lines. Six faces because there's six faces on the Cube. So for the face is parallel to the field lines. These four no few lines into her exit because the field lines are going like this. This is the face of the block, so none of them were going in or out of that face. So that means for the four pecker low faces, the electric flux is zero cool. So now we just have to figure out what is the better. What is the electric flux for the perpendicular faces? We have two of them, right? So this would be like this face that it enters in the office of one that is exiting. So one of the faces, As I said here has enough field lines and during it, and the other one's gonna have it exiting. So then we also know the net has to be zero. So there gonna be equal and opposite So we can say the electric flux in equals, the negative electric flux out because we already said the Netflix has to be zero, and these are the two perpendicular faces, so we know that's how they're given. So now Let's find the electric flux entering, and this is given as the magnitude of the electric field times the area. The area's el squared because it's a Cuba side length L in and now times Deco sine of the angle between them. So if the angle is coming or the area vector is coming out normal to the surface, that means the angle between these they're gonna be at 1 80 degrees. The angle for these, they're going to be early album. Is that gonna be a zero degrees? So this co sign of 1 80 is negative one. So that means this is negative being R l squared and based on our relation above, we know that the electric flux on the out face must be the opposite of this or be not l squared, which we also would have seen because coastline would have the data would have been zero degrees and co sign of zero degrees is positive one. So it all checks out. So there is the one face. Here's the other face, and all the other four are zero Russell

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