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$\bullet$$\bullet$ If two electrons are each$1.50 \times 10^{-10} \mathrm{m}$ from a proton,as shown in Figure $17.41,$ findthe magnitude and direction ofthe net electrical force they willexert on the proton.

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Physics 102 Electricity and Magnetism

Chapter 17

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Cornell University

Rutgers, The State University of New Jersey

University of Winnipeg

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.

04:08

$\bullet$$\bullet$ If two …

02:02

If two electrons are each …

0:00

04:50

13:03

05:00

03:11

04:26

An electron is a subatomic…

A proton moves with a spee…

01:30

(I) A proton is released i…

02:07

Two protons in an atomic n…

02:17

and this problem. We want to figure out the net force on this positive charges. And so we have a Force F one pulling it to the right, and we have a force of two pulling it up at an angle 65 degrees. With respect to the war zone, these two forces will be the same in magnitude, since the charges on the end of each will be the same and then the distance our is also the same between them. So let's calculate that magnitude. So F one is equal to have to just the magnitudes here and it's equal to K Time's Q on Q too over R squared. Well, this is just equal to K e squared, since both charges here have absolutely charge he for our school. And now he is known constant casing on constant ours, given in the problem. So we can solve this to get 1.23 times 10 to the negative eight noons. Now that we know that we need to break up each of these forces into its X and Y components where the X in my directions are shown here and so let's go ahead and bring down this 1st 1 F one, which is this horizontal force here in the extraction is just equal to the full force. Since it's fully pointing in the extraction. This's 1.23 times 10 to the negative eight News and F one Why? Which is like 10 nunes F two x, which is this guy is going to have non zero x and Y components and scum. You're related to the angle here. And so I have to Axe is equal to have to times go sign 65 degrees because that is the horizontal component. And this is, uh, being 4.32 times 10 to the negative nine noons and F two. Why is just equal tio two times signe of 65 degrees. And so this is equal to 9.2 son times 10 to the negative nine Nunes. And now I can add the ex components about these forces to get the result into X component. And so FX is able to f one x plus after Max and these are on the page and I just uris this one here. So these two numbers here combined to give 1.46 times 10 to the negative eight noons now. Similarly, if y is equal to F one lie, let's have two. Why? And adding These, too gives 9.27 time stands the name nine new ones. The resultant Magnitude Force F is equal to squared of FX squared plus F y squared. And when we play the same, we should get our original left that we found in the problem. And so playing this in, we get 1.73 times 10 to the negative eight noons. So this is the magnitude of the resultant force from both F one and 1/2 to and so figure out the angle that's directed. And we can say that the tangent of data is equal to that fly over FX, and we know f flying effects. They're just here and so feeling those in give 0.6349 and then taking the inverse tangent will give us the angle so theta is equal to 32.4 degrees, so the resultant force will have magnitude. This and we'll be angled at 32.4 degrees with respect to the horizontal, and that completes the answer

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