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Two long parallel transmission lines 40.0 $\mathrm{cm}$ apart carry 25.0 $\mathrm{A}$ and 75.0 A currents. Find all locations where the net magnetic field of the two wires is zero if these currents are in (a) the same direction, (b) opposite directions.

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Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 20

Magnetic Field and Magnetic Force

Motion Along a Straight Line

Motion in 2d or 3d

Electric Charge and Electric Field

Gauss's Law

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

University of Winnipeg

Lectures

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.

04:28

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H. The term "magnetic field" is often used to refer to the B field. In a vacuum, B and H are the same, whereas in a material medium, B is a component of H. In the latter case, H is the "magnetic field strength", and B is the "magnetic flux".

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Two long, parallel transmi…

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II Two long, parallel tran…

05:48

Two long, parallel wires s…

02:54

Two long, parallel wires a…

05:42

Two long, straight, parall…

10:46

Two long, parallel wires c…

04:39

Two long insulated wires l…

01:54

Two long parallel wires ar…

02:50

So the question is asking us to find locations where ah, being met of the two wires is equal. Teo zero Tesla's. Ah, we also know that the magnitude of the magnetic field is equal to mu, not the primitive, the magnetic permeability of a vacuum times. Or we can say primitive ity free space times the current divided by two pi r. So, at this point, we can say for part A we need to weaken Dr S O going into the page. Is I sub one? And then we could draw dash line to ice up to and then going straight in the middle. Well, rather closer to ice up one here. This distance right here, we're goingto label us X. We're actually gonna make this a bit shorter. Um, going straight down is beasts up to going straight up his piece of one. And this distance right here, we're going to label as point 400 meters minus X, and we can say point P is here. So at this point, we can say that the on ly thing that we really need to relate is the r term, so we can say that new I said no and the different magnitudes of the doing So mu not times thie current divided by two pi X. We can say that this is going to be equal to mu, not times Thie currents up too divided by two pi 0.4 minus x. And at this point, we know that this is going to be 25 over X. This is an equal 75 divided by point for minus X. And you can use the sol function in your teeth for 85 for 89 in order to solve for X Uh, and we find that axe is going to be equal to 0.100 meters. However, you could find this. These is simply three ah 25 satisfied or by 25 25 to 3 s O if X is 0.1 0.4 minus 0.1 would be 0.3, and both of these fraction would be equal seeking just solving your head. However, you can also use the cellphone trace on your calculator. You conceives a sole function on your calculator from the very beginning if you would like, but it's a lot easier to simplify it as much as you can. But again for party, the answer is X equals 0.100 meters. Now for part B. Um, let's draw the diagram. Ah, again, we have this dashed, all right? And we can say right here this is going to be into the page ice of one and then here, completely straight out of the page. It's gonna be ice up to the gist here, going straight down his piece of two going straight of this piece of one and the distance between the axis and ice up to his ex. And then, ah, we can say that this distance right here not to scale is 0.400 meters. So at this point, whether points or the floor my posse point 0.400 meters. Okay, At this point, we can say that mu not times ice of one divided by two pi X is going to be equal to mu, not times. Eyes up to divided by ah two pi times point for plus X. So party was point for minus X. Part B is 0.4 plus x again this unequal 25 divided by ax This illegal 75 divided by point for plus X and so here we know that if we use the sol function on your 84 85 89 we know that X is going to be equal to 890.200 meters. So this would be your answer for part B. Again, these distances simply denote the location or the net. Magnetic field of two wires is equal to zero. Tesla's. So again, these do not forget, I guess, the importance of what we're trying to find the X value. However, these are critical X values. That is the end of the solution. Thank you for watching.

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