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A point charge $Q=+4.60 \mu \mathrm{C}$ is held fixed at the origin. A second point charge $q=+1.20 \mu \mathrm{C}$ with mass of $2.80 \times$ $10^{-4} \mathrm{kg}$ is placed on the $x$ axis, 0.250 $\mathrm{m}$ from the origin. (a) What is the electric potential energy $U$ of the pair of charges? (Take $U$ to be zero when the charges have infinite separation.) (b) The second point charge is released from rest. What is its speed when its distance from the origin is (i) $0.500 \mathrm{m} ;$ (ii) 5.00 $\mathrm{m}$ ; (iii) 50.0 $\mathrm{m} ?$

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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

Simon Fraser University

Hope College

University of Sheffield

University of Winnipeg

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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A point charge $Q=+4.60 \m…

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$A+2.00-n C \quad$ point c…

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A $+$2.00-nC point charge …

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A +2.00 nC point charge is…

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$A \quad$ positive point c…

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06:48

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Hey, so when this problem, we're told that a point charge is that the origin? So here is Q Q is plus 4.60 times 10 to the minus six cool ums. And here it is it the origin and then the 2nd 1 is placed 10.25 at a position of 0.25 from the origin. So that's this Q. And that's 1.20 micro cool ums. And then that's it. And then this particle also has a massive 2.8 zero times, 10 to the minus four kilograms. So here is our cue, and then our other Q 0.25 is this distance, and then we're trying to obtain the electric potential energy of the pair. So that's just gonna be, um this is probably a formula in the book. Que que que over our. So I'm gonna plug that into a calculator. I have obtained 0.199 drools. And for part B, um, we're told that the second particles released from rest and we want to know the speed when it's had these different distances from the origin, so I'll just go ahead and record those distances So be our distances are 0.5 meters. These opposite sign charge charges. Um oh, yeah, they're the same size. Okay, so repel. So 0.5 and then five and then 50 loops one, too. And then three. So for this, we want to use that the cheating If there's, uh, no work being external work being done on the system than the change in kinetic energy is equal to minus the change in potential energy by energy conservation. So whatever is lost on potential is gained in kinetic energy. And so we need to find the change in potential energy for boo for all these positions. And then, um then me Senate equal to the kinetic energy. And then we have, ah, formula for the velocity. So, um, just double check. What is it? Speed? Yeah. So I'm gonna come up with the general formula. So this is 1/2 Connecticut RG. It's released from arrest. The change in kinetic energy is 1/2 of the final squared minus. Um, you final minus hoops. Not be. You initial. Sorry. That's supposed to be a you. Let's see. I'll try the you one more time and so v is equal to therefore the square root of two divided by, um, times. Um, you final when issue initial, um and then you final is gonna be We need to follow the formula for potential energy. This cake you, Cooper, are So that's this Kay Q Q divided by our And so, um, we'll be using the R's listed up here. So these are all my arms for all these different cases. And so ask minus yes, issue initial. So I'm gonna go ahead and plug all of these into a calculator and get answers. Tall possums video. Okay, so I just planned everything into a calculator, and then I obtained that the velocity for the 1st 1 the 10.5 meters is 26.6 meters per second, and the velocity for the five meters is 36.7 meters per second. So it's gaining speed as it's moving further and then finally 37.6 meters per second. Once it's at 50

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