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A small particle has charge $-5.00 \mu \mathrm{C}$ and mass $2.00 \times$ $10^{-4} \mathrm{kg} .$ It moves from point $A,$ where the electric potential is $V_{A}=+200 \mathrm{V},$ to point $B,$ where the electric potential is $V_{B}=+800 \mathrm{V} .$ The electric force is the only force acting on the particle. The particle has speed 5.00 $\mathrm{m} / \mathrm{s}$ at point $A .$ What is its speed at point $B ?$ Is it moving faster or slower at $B$ than at $A$? Explain.

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7.416$m / s$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 18

Electric Potential and Capacitanc

Kinetic Energy

Potential Energy

Energy Conservation

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

University of Washington

Simon Fraser 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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So for this question, we're told that a small particle has a charge of five times 10 to the minus six cool ums. And it has a mass of 2.0 times 10 to the minus for grooms. Our killer Grams, I'm gonna fix this funny exponents. So this should be a six. And it moves from a where the electric potential is 200 volts to be where it's 800 volts. So v a is 200. Envy B is equal to 800 volts and the forces acting on the particle and then this particle has a speed. I've, um So it's five meters per second and a and then our goals. Who got what is this speed? I'd be so I'll write that down. Oh, this is confusing. So this is little V at a busy girl of five point Ooo meters per second. And then our goal is to get little V B equals question work. So, um, if we have a charge moving within this potential, um, see, he's gonna the track. Is there any other information about the potential? So is it, um is a potential changing linearly? Well, I guess you know, you don't even need that information because of this sort of path independence thing. So for this problem, I think you want more. So use the principle that the change in potential energy the magnitude of the change of the potential energy. Actually, we shouldn't probably not use magnitude since where we care about if it's losing or gaining. So so the work done on a particle, I'll go back to that. The work done on a particle is equal because there's a couple ways to think about it. So I'm gonna think about it as, um, there's no I like to start off energy problems with the statement that, um W nut external. So the net external work done on a system is can contribute to a change in kinetic energy, where are changing potential energy? So I'm gonna say that the, um, electric forces internal so I'll say that this thing is zero. And so we get the equation that the change in kinetic energy is equal to minus the change in potential energy, and so the so let's go ahead and fill in either these sides. So the change in kinetic energy so it's starting at a so it's one happen via a squared or sorry. It ends, actually, so it should be changing. Kinetic energy is final minus initial. So you want to have its final state. So, um, so then that's gonna be the B minus 1/2 Um, the eh squared, and then that's minus the change in potential. So that's que que final are divided by our final. So forget this little line here, um, minus the initial. So that's Kay Q over our initial. And so our goal is to solve for Phoebe So the B is gonna be equal to Oh, I realize we don't even need this type of formula. Um, that's just gonna be, um, so you we just want to use the fact that you is Q b sexually. Sorry. Let me rewind a little bit given, um, what we have so change in. So we want to use the formula that generally change in you is Q change in V. And so, um, we can just say that changing you is cute. Changing rien be final minus B initial. The final state is B, so it's gonna be Q via B minus fia Oh minus V A Great. Um, it's okay. Now, Aiken saw for Phoebe. Phoebe, we just want to bring this to the other side. Um, so bring that term to the other side, and then we got V b is gonna be so I know. Well, I know multiplying everything by times two divided by, um, And then we'll end up squaring the whole thing. So that's just gonna be two AM times. Um, plus 1/2 M v a squared minus. Q B B minus V a. Okay. And then now I'm gonna go ahead and put this into a calculator. Okay? So when I put this into a calculator, I am thine that it was seven point for 16 meters per second.

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