Lines Definition and 1000 Threads

Does a positive test charge follows along the path of electric field lines if it is free to do so? I mean the trajectory of the charge is along the electric field lines and the field lines are not necessarily straight.

This question occurred to me a few days ago and it's been bugging me ever since. Consider a circle in the coordinate plane with center P(x,y) and radius R, where R < D, D being the distance from the origin to the circle's center. There are two lines tangent to the circle (T1 and T2) that pass...

I’m confused: Long distance electric power lines are modeled with distributed impedance and are therefore modeled as transmission lines. Long distance electric power lines are considered to be a two wire line (for a single phase of the electric power line anyway). What other types of...

stuck on how to simplify this?

What would be the point of knowing information about the subtangent and subnormal lines? Do they have any worthwhile real-world applications? Wikipedia says that they are archaic and fell into disuse after the early 20th century. Thank-you

Homework Statement The problem asks me to evaluate the angle between these two lines: ##r : \begin{cases} x - 2y - 3 = 0 \\ 3y + z = 0 \end{cases} s : \begin{cases} x = 1 + 4t \\ y = 2 - 3t \\ z = 3 \end{cases}## both oriented to the decreasing ##y##. Homework EquationsThe Attempt at a...

It isn't difficult to find the electric field of a dipole. However, it is tricky to find the field lines. All points of a field line have to be parallel to the electric field at those points. A tangent, which is the derivative, is parallel. We can hence formulate the equation for a field line...

Homework Statement Sketch the graphs of y=x2 and y= -x2+6x-5, and sketch the two lines that are tangent to both graphs. Find equations of these lines. Homework EquationsThe Attempt at a Solution So I know that a tangent line to both graphs means that the tangent line will touch the first graph...

Homework Statement Proof that if the slopes of two lines a1, a2 (that are not vertical), m1,m2 satisfy: m1*m2 = -1, then the lines are perpendicular. Homework EquationsThe Attempt at a Solution I tried to use the tan function, so that m1 = tanΘ where Θ1 is the angle of the line formed from x...

Hi. An electric dipole field (two opposite point charges separated by some distance) has fields lines from the positive to the negative charge, but also field lines reaching to and coming from infinity. Starting from the positive charge, is there a way to compute the opening angle of the cone...

Homework Statement Refering to this exercise I started https://www.physicsforums.com/threads/checking-if-the-following-lines-are-coplanar.885948/ I now have to find the plane containing the two intersecting lines and the plane containing the two parallel lines. In the case of the parallel...

Homework Statement So, I'm doing a long exercise, you can check here the first part: https://www.physicsforums.com/threads/checking-if-the-following-lines-are-coplanar.885948/ The second part asks me to find, if one of the couple of lines are skew, the orthogonal line to two skew lines...

Homework Statement Set an orthonormal reference system in the euclidean space ##E^3## and consider the following lines: $$r: \begin{cases} x = 3 \tau \\ y = 1 + \tau \\ z = 3 - 2 \tau \end{cases}s: \begin{cases} x + z - 4 = 0 \\ x - 3y + z + 2 = 0 \end{cases}t: \begin{cases} 4x - 2y + 5z - 3 =...

Homework Statement We are suppose to make a lab report about and experemint that we did in physics lab. It consisted of drawing equipotential lines in a overbeck electric field mapping apparatus. Different desing plates were used, each having conductors, some were circular and other where...

Homework Statement Hi, I have a question about my lab report that I am doing. The only question that I am having problems to understand is the first one, it says, "why are the equipotential lines near conductor surfaces parallel to the surface and why are they perpendicular to the insulator...

Homework Statement Let A, B and C be distinct vectors in V3 with B and C non-parallel. a. Find an equation for the plane containing both the line through A parallel to B and the line through A parallel to C. b. Verify that the two lines actually lie in the plane. Homework EquationsThe Attempt...

Hello. I'm now taking accelerator physics class and the lectures said in the thermionic electron gun, anode metal mesh should be grounded in order to prevent electrons which traveled beyond the mesh from coming back due to the electric field lines. Without grounding of the anode, I believe...

Dear all, I have lately been interested in AI. One of my thoughts has been as follows: What if we have two 'neurons' and the world consists of vertical, horizontal and diagonal lines. How would we go about making sure only one neuron is assigned to either vertical or horizontal lines and...

I was reading this article on Wikipedia about single phase generators and the operation of a basic generator, and I'm having a very difficult time understanding what is meant by cutting lines of force and how the rotating armature being perpendicular to the field cuts zero lines. While when it...

Hi everyone. I am told to find the equation of the tangent plane to the surface x^2 + 2xy^2 -3z^3 = 6. I do not know how to approach this problem, and I was wondering if anyone would be kind enough to help. I know that for example if I had an equation z = x^2 + y^2, with a point P(x0,y0) and...

Hi everyone. I was working on a problem for days. The problem statement is: "Consider points P(2,1,3), Q(1,2,1), R(-1,-1,-2), S(1,-4,0). Find the shortest distance between lines PQ and RS." Now, I did the following formula: PS dot (PQ x RS) / magnitude of (PQ x RS). (For skew lines) Now...

Hello! Please help me understand whether I'm going to the right direction with the solution or partially wrong or completely wrong. I have a basic Fluid Mechanics course at the uni, the following problem is from a past exam my teacher gave us to practice before the exam, so there're no answers...

The graph of which of the following equations is a straight line parallel to the graph of 3y-1=2x? A: -3x + 2y = -2 B: -2x + y = 6 C: -2x + 2y = 3 D: -x + 3y = -2 Can you show the work when you answer please? Thanks

I set up a Twin Paradox scenario and accompanying spacetime diagram to help better understand the resolution, but I had a question about the diagram I was hoping someone here could help answer. Please excuse the hastily drawn diagram! (Note: the ' frame corresponds to the outbound trip, the...

What is the cause of hyperfine line splitting? I saw somewhere that it was because of spin quantum number and somewhere else that it was because of how electrons interact in the atom. And relative intensity of spectral lines? I'd assume it's due to the probability of electron jumps being more...

sir, we know that the electric field lines are perpendicular to the surface of the conductor ,it means charges are rest on the surface of the conductor ,there is no work done. if we create an electric field such that the electric field lines are at a different angle to the surface of the...

Hi, I realized I didn't understand the physical model of something I know the theory of pretty well. I was considering the real power loss of an AC transmission line I2*R, then I realized that from source to load the electrons in an AC line don't actually move anywhere. (as far as I know) Yet if...

Homework Statement A diffraction grating gives a second-order maximum at as angle of 31° for violet light (λ = 4.0 × 10^2 nm). If the diffraction grating is 1.0 cm in width, how many lines are on this diffraction grating? Homework Equations d = (m)(λ)/sinθm The Attempt at a Solution d =...

I have no idea how to solve this problem. ABCD is just an irregular Quadrilateral so nothing too special with that figure. We are looking for the ratio BC:CD and we only have that two angles. I know that the answer is 1:√2, but I have no idea how to find it.

Hi, I have a question concerning the use of aluminium in power lines. I know that it's lighter than copper and thus cheaper, which is the main reason we prefer it above copper. But in fact alumunium has a lower conductivity than copper. Why is it then that one kg of aluminium can carry twice...

Morning all, I am currently designing a VAWT and am working on a contra-rotating turbine, but I am extremely new to electrical engineering as a whole, I just really like the idea of designing something like this as a fun project and possibly being able to benefit from lower power bills as a...

Hi, I wonder what would the path of magnetic field be in my case.I have a solenoid , it's a metal rod that has a winding in the middle of it, I need the magnetic field to come out of the rod not at the ends of it as is usually shown in pictures but at the surface side along each end of the metal...

Here's a question that's been on my mind for a while (I use c#) does the number of lines in your program affect the speed of your program? Let's say you had a program that skipped over one trillion lines, and another who skipped over ten lines. The lines could be inside an if statement who's...

who was the first person to discover how to measure the wavelength of absorption lines in the solar or stellar spectra and what method was used?

Homework Statement On the picture, ##ABCD## is a parallelogram, ##(EF) // (AB) ##, and ##(GH) // (BC)##. The problem is : show that lines ##(EB)##, ##(HD)##, and ##(IC)## either all meet in ##M##, or are parallel. Homework EquationsThe Attempt at a Solution I've solved the problem...

Homework Statement I am not sure i know what is meant by the input load line and the output load line in parts b and c. I tried looking it up in my book (fundamentals of microelectronics by razavi) but to no avail. Any help is appreciated.

Homework Statement 9. Suggest a realistic scenario that could be modeled with each of the following equations. Be sure to define each variable, including units. 2. Homework Equations y=mx + b The Attempt at a Solutiona. y = –65x + 200 To stay at a private golf course, you have to pay a...

I think its a defination to have infinite longitudnal lines , if line are not perpendicular than the infinite point will not add up to give the circumferance of equator, please help

Homework Statement Okay thanks everyone for taking the time to read this quesiton. Now I sort of know how to do this question but I am not entirely sure how I should approach it: I have points A(2,1,2) B(3,2,-1) C(-1,2,4) and D(-2,1,3) Now a line passes through points A and B and also C and...

Homework Statement I am having problems with the second part of the question - proving that the relationship given is true. Homework Equations See question. The Attempt at a Solution Firstly, consider a single pair of transmission lines with characteristic impedances ##Z_{1}## and ##Z_{2}##...

Homework Statement My textbook says that high voltages are used for power transmission because according to the equation P=VI and P= I2R, power loss can be reduced. What confuses me is why the equation P=V2/R cannot used here? And if used, would be contradictory? I know that R is the...

Homework Statement A metal sphere of charge +6μC is surrounded by a metal shell of net charge +6μC. Which of the following diagrams represents the electric field lines of the system? Homework EquationsThe Attempt at a Solution The correct answer provided by my teacher is a figure with 12...

Hello! Please help me with this question. I'm currently studying Light and Geometric Optics and have become quite confused. When looking at diagrams of mirrors, and light relfection into eyes, why is it that eyes only see things when tracing the light in straight lines? For example, if an...

An interesting article on the connected nature of things on the internet: http://arstechnica.com/information-technology/2016/03/rage-quit-coder-unpublished-17-lines-of-javascript-and-broke-the-internet/

I am trying to find the field lines of the 3D vector function F(x, y, z) = yi − xj +k. I began by finding dx/dt =y, dy/dt = -x, dz/dt = 1. From here I computed dy/dx = -x/y, and hence y^2 + x^2 = c. For dz/dt = 1, I found that z = t + C, where C is a constant. I am unsure where to go from...

My question regards finding the field lines of the 3D vector function F(x,y,z) = yzi + zxj + xyk. I was able to compute them to be at the curves x^2 - y^2 = C and x^2 -z^2 = D, where C and D are constants. From my understanding the field lines will occur at the intersection of these two...

Homework Statement Find the angle between the straight lines: ##(x^2+y^2)(\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta})=(x \tan{\theta} - y \sin{\alpha})^2## Homework Equations [Not applicable] The Attempt at a Solution Dividing by ##x^2##, ## (1+(\frac{y}{x})^2)(\cos^2{\theta}...

Homework Statement In a specific area of the space, an electrical potential is given as: \begin{equation} V(x,y,z) = A(2x^2 - 3y^2 - 3z^2) \end{equation} where A is a constant. a.) Determine the electrical field E for any given point in the area. A test charge q_0 is moved from the point...

It just occurred to me that akin to electric power lines, which in the end just connect a voltage differential over a long distance and facilitate power exchange between the two end points, one could build "thermal power lines". That is, a well-insulated cable that internally consists of a...

Hi, I am curious as to whether there is a relationship between field lines and magnitude of charge. For instance, is the sketch for the electric field of a +1.0 micro coulomb charge the same as the sketch for a +2.0 micro coulomb charge? Thanks. All help is very much appreciated!