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(II) In a certain region of space, the electric field is constant in direction (say horizontal, in the $x$ direction), but its magnitude decreases from $E=560 \mathrm{N} / \mathrm{C}$ at $x=0$ to $E=410 \mathrm{N} / \mathrm{C}$ at $x=25 \mathrm{m} .$ Determine the charge within a cubical box of side $\ell=25 \mathrm{m}$ where the box is oriented so that four of its sides are parallel to the field lines (Fig. 28).

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$Q_{\text {enclosed}}=-8.3 \times 10^{-7} \mathrm{C}$

Physics 102 Electricity and Magnetism

Chapter 22

Gauss's Law

Electric Charge and Electric Field

Electric Potential

Lesma R.

September 16, 2021

La velocidad de un móvil que recorre una recta dada por v=t^2-10t+9m/s cuando t=0seg ,x=2m para el intervalo de tiempo desde t=0seg hasta t=5seg determine: a) el grafico aproximado de la trayectoria , b) el desplazamiento , c) la distancia recorrida

Cornell University

Rutgers, The State University of New Jersey

Hope College

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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we're in Chapter 22 problem nine here, it says In a certain region of space, the electric field is constant in a direction. The positive X direction but its magnitude Magnitude decreases from E X equals zero to thief 5 60 Newtons per Coolum and E X equals 25 meters is 410 Newtons. Coolum So determined. The charge within a cubicle box of side links 25 meters where the box is oriented so that the four size before of its size are parallel to the field. Lighten. So that means only this face here and the opposite face that we can't see are the ones with perpendicular field lines to them. So that means they're the only two that contribute to the flux. So we can write the total flux has e dot a for the left face plus e a for the right face. So this becomes E for the so for the left face, it is entering the box, which means it's going to have a negative fucks and e for the right faces incident. So it's gonna have a positive flux, and we know the area is just l squared. So we're gonna be left with e, right? Because that's the positive one. Times squared, minus E left times l squared. So that means our flux here is given as delta e times l squared. Just that Delta e being the right minus the left. So now we can rearrange this to find the charging clothes using Telesis Low. And this is now Delta E. That was squared. Absolutely not. So it's plugged this in. This is 100 and 50. All right now, Mrs Right minus left. So right. It's 410 minus 5 60 So this is negative. 1 50 is delta. He times 25 meters squared times 8.85 times two to the negative 12 way plug All that in. We see that this comes out to being the charge enclosed of negative 8.3 times 10 to the negative seven columns. Awesome. That's it.

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