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$\bullet$$\bullet$ If a proton and an electron are released when they are$2.0 \times 10^{-10} \mathrm{m}$ apart (typical atomic distances), find the initialacceleration of each of them.

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$\begin{aligned} a_{\text { protom }} &=3.45 \times 10^{18} \mathrm{m} / \mathrm{s}^{2} \\ a_{\text { electron }} &=6.334 \times 10^{21} \mathrm{m} / \mathrm{s}^{2} \end{aligned}$

Physics 102 Electricity and Magnetism

Chapter 17

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Cornell University

Simon Fraser University

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.

01:19

If a proton and an electro…

05:03

01:04

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01:21

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04:54

Two protons each of mass $…

03:04

05:58

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06:20

01:26

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in this problem when used this force law in order to figure out the force between the electron and the proton. And they were going to use Newton's second law to figure out the acceleration that the electron and the Proton experience. And so we're gonna let Kyu won be the proton here and you to be the electron. So if you want is equal a positive in queue to physical to negativity and so the absolute value of them multiply together, we'll give us he squared. And this information down here will be helpful in the second half. The problem when we're actually calculating the accelerations and so playing this into F and solving for F because this K he squared over r squared and were told with ours, and we know he is. It's just Constance those k and so this gives us 5.75 times 10 to the minus nine Newtons. Now this force is shared by the electron and proton. So the electron pulls on the proton with this force in the proton pools on the argument with this force and this is attractive. It's attractive because you wanting que tu or different signs So that's why I was attractive in this interactive force. And so, in order to actually figure out the accelerations, we're going to use me in second long with these masses. And so the acceleration of the proton is equal to this force we just calculated over the mass of the proton and the force that we just calculated is 5.75 times 10 to the minus nine. Noone's, which is an S I s units and the mass of a proton is right here. And so it's 1.67 times 10 to the minus 27 and this is in kilograms. When you do this out, you get that deceleration of protection is 3.4 time stand to the 18 meters per second squared, so it's very, very fast. Acceleration of the electron is equal to the same force because they both experienced the same force. But this time it's over the massive electron, which is much smaller than the massive proton. So the numerator will be the same as before times tense in last night, Newton's. But now the denominator will be this guy. And so it's 9.11 Time stands the nice 31 killer rooms doing this. L It's 6.3 times 10 to the 21 years for saying squared, and this completes the answer. But notice how the exertion of the election on is three orders of magnitude greater than the acceleration of the proton, even though they experience the same force. And the reason is that the electron is much lighter. So the same force on a much lighter object produces a much greater acceleration, which is the gist of Newton's second law to being with.

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