What is Arc: Definition and 485 Discussions

An electric arc, or arc discharge, is an electrical breakdown of a gas that produces a prolonged electrical discharge. The current through a normally nonconductive medium such as air produces a plasma; the plasma may produce visible light. An arc discharge is characterized by a lower voltage than a glow discharge and relies on thermionic emission of electrons from the electrodes supporting the arc. An archaic term is voltaic arc, as used in the phrase "voltaic arc lamp".
Techniques for arc suppression can be used to reduce the duration or likelihood of arc formation.
In the late 1800s, electric arc lighting was in wide use for public lighting.
Some low-pressure electric arcs are used in many applications. For example, fluorescent tubes, mercury, sodium, and metal-halide lamps are used for lighting; xenon arc lamps have been used for movie projectors. Electric arcs can be utilized for manufacturing processes, such as electric arc welding and electric arc furnaces for steel recycling.

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  1. J

    Arc Length of 1st Full Turn of Archimedean Spiral

    Homework Statement 27. Use the parametrization x = tcost, y = tsint of the Archimedean spiral to find the arc length of the first full turn of this spiral (corresponding to 0 <= t <= 2∏ ). Homework Equations The Attempt at a Solution I use onenote and a tablet, so my exact attempt in in the...
  2. M

    Calculating the arc length in r^3

    Homework Statement r(t)=ti+2tj+(t^2-3)k or r(t)=(t, 2t, t^2-3) 0≤t≤2 Homework Equations arc length formula ∫[the scalar of dr/dt] I know I can calculate the arc length through the equation above, but the questions asks for me to utilize this formula. ∫√(t^2+a^2) dt =...
  3. A

    Arc length problem with a thorny integration

    Homework Statement So, the question gives a particle traveling over a path \gamma, and I need the arc length. Homework Equations The path is \gamma(t) : [1,4] \to ℝ^3, t \mapsto (t^2/2, t, ln(2t)). We want the arc length over 1 \le t \le 4. The Attempt at a Solution First, the...
  4. M

    Find the arc length of the curve (Polar)

    Homework Statement I was wondering if I did this problem correctly as I don't have the solution, also wanted to make sure that my limits of integration were correct as they tend to be tricky in finding arc length in polar coordinates. x(t)=arcsint y(t)=ln(sqrt(1-t^2)) Homework...
  5. Y

    Finding arc length of vector valued function

    Homework Statement Find arc length of the graph of r(t) = ti + ( (t6/6) - (6/t4) )j + t√3 k 1≤t≤2 Homework Equations Arc length = ∫ ||dr/dt|| dt (Integral from t0 to t1 of norm of derivative of r) The Attempt at a Solution dr/dt = i + (t5 + 24/(t3) )j + √3 k 12 = 1 (√3)2 = 3 (t5 + 24/(t3)...
  6. O

    Computing arc length in Poincare disk model of hyperbolic space

    I am reading Thurston's book on the Geometry and Topology of 3-manifolds, and he describes the metric in the Poincare disk model of hyperbolic space as follows: ... the following formula for the hyperbolic metric ds^2 as a function of the Euclidean metric x^2: ds^2 = \frac{4}{(1-r^2)^2} dx^2...
  7. A

    Speed of electric spark, arc and conductive ionized gas

    Dear colleagues, If an arc or a spark traveling in vacuum is actually the electrons jumping across vacuum, do they travel at near light speed? From another point of view, devices like thyratrons use ionized gas molecules to conduct electricity, at what speed are those ionized molecules...
  8. A

    Help balancing an unequal lever thru an arc - (Foldover flagpole)

    I am constructing a pipe flagpole that instead of using a rope or wire to run the flag up, has a pivotrod or axel near the bottom (fulcrum point) that allows the entire pole to be pulled down when unlocked. The Idea is that you attach a piece of chain a ways up the pole and use it to pull the...
  9. H

    Arc length & area of surface of revolution

    Hi everyone! I have two questions, one about area of surface of revolution and another is about arc length... I really fail to do this two question despite many times of trying so I hope someone can help me 1. Find the area of the surface of revolution generated by revolving the arc of the...
  10. D

    Checking if a point is on an arc, defined by two vectors

    So, i have a point in the coordinate system, and an arc defined by two vectors of equal length starting in the same point. The arc is always smaller than 180. How would i check if the point is on the arc? (the point is always on the circle, just need to check if it is in between these two...
  11. A

    How do I obtain a usable 60 volts for my singing arc?

    Alright, so I'm building the singing arc that's in this schematic. http://www.volny.cz/jmartis/flyback_singingarc.png Now my first problem is obtaining a 60 volt input. Will I get a usable 60 volts (consider current spikes) if I bridge rectify a 120 volt wall current, obtaining a -60 and...
  12. E

    Arc Length and Surface question about hyperbolic function

    If the circumference of the region bounded by the curve y=cosh(x) and the lines y=0 x=a and x=-a is 2a+4, where a>0 find the area of the surface obtained by rotating the part of the curve y=cosh(x) between x=a x=-a and around the x axis. This is my homework question.I tried to solve it.I...
  13. S

    Arc length and definite integral

    Hi everyone ... I am a first time poster from South Africa. I have been visiting the forum for some time. I am busy teaching myself calculus and physics. I have hiccup with the concept of definite integral and arc length of a function. In my understanding these should be the same thing...
  14. J

    Can one burn aluminium wires using an electric arc?

    Could one burn aluminium wires by striking up an electric arc between them and then feeding them towards each other as they are consumed (like an arc light)? I assume the aluminium oxide would be burnt off as a vapour by the high temperature of the electric arc and thus would not inhibit the...
  15. S

    Arc Length of Ellipse, Hard Integral

    Homework Statement Find the arc length of the ellipse or deformed circle. r^2=x^2+(y/β)^2 r=radius β=dilation constant k="random" constant Homework Equations The Attempt at a Solution I suspect it's impossible but I can't prove that. After working it out I got stuck with these...
  16. M

    Iron Man's Arc Reactor Technology

    The Marvel Avenger's Movie is coming out in a month's time. While many superheroes like the Hulk and Spiderman require much more biological research to come true, superheroes like Iron Man, Batman, Black Widow rely on engineering technology. Which of our current-day technology has the...
  17. D

    How Do You Calculate the Arc Length of y = ln(x) from x = 1 to x = e?

    ∫Homework Statement Use the integration tables to find the exact arc length of the curve f(x)=ln x 1≤x≤e Reference the table number formula used Then approx. your answer and compare that to the approx. "straight line distance" between 2 points coordinates of two points...
  18. ArcanaNoir

    Integral of unit tangent vector equals arc length?

    Homework Statement Let c(t) be a path and T the unit tangent vector. What is \int_c \mathbf{T} \cdot d\mathbf{s} Homework Equations The unit tangent vector of c(t) is c'(t) over the magnitude of c'(t) : \mathbf{T} = \frac{c'(t)}{||c'(t)||} The length of c(t) can be represented by ...
  19. lonewolf219

    Why electric potential of arc treated like point charge

    Homework Statement Give an expression to find V of Arc of uniform charge (at the center, or origin) Homework Equations V=kQ/R The Attempt at a Solution the solution is kQ/R. I'm wondering why an arc can be treated like a point charge... Is this reason partly connected to a...
  20. V

    Computing Arc Length and Cannot Solve the Integral

    Homework Statement Find the length of the polar curve. Complete the cardioid r=1+cosθHomework Equations L=∫αβ√[f(θ)2+f'(θ)2] dθ The Attempt at a Solution Given f(θ)2 is equal to cos2θ+2cosθ+1 and f'(θ)2=sin2θ I arrive at the integral ∫αβ√[2cosθ+2] dθ which I cannot for the life of me...
  21. M

    Reparametrize the curve in terms of arc length

    Reparametrize the curve R(t) in terms of arc length measured from the point where t = 0 R(t) is defined by x = et, y = \sqrt{2}t, z = -e-t Arc length S = ∫ ||R'(t)||dt ||R'(t)||= sqrt{\dot{x}2 + \dot{y}2 + \dot{z}2}The attempt at a solution Getting R'(t) ==> x = et, y = \sqrt{2}, z = e-t...
  22. A

    Chain rule violated for arc length?

    ->ds/dt where s is the arc length in cartesian coordinates is ((dx/dt)^2+(dy/dt)^2)^(1/2). -> Therefore by the chain rule ds/dt = ds/dp * dp/dt, but if I substitute dx/dt=dx/dp* dp/dt and dy/dt= dy/dp* dp/dt in the formula above, I get ds/dt=ds/dp * |dp/dt|?? What is happening? ->Even by...
  23. L

    About the denomination of an elliptic arc

    Hi all, Does anyone know the specific names of the high-curvature arc and the low-curvature arc on an ellipse? Or, do they have special names after all? Anyone help me figure this out, thank you very much! Regards.
  24. U

    How to find the radius of a circle by knowing two points and its arc length

    How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to solve for a trigonometric equation or is there any algebraic or geometric method?
  25. K

    Integral - Length of cardioid arc question

    Homework Statement Hey all, I'm trying to calculate the length of the cardioid r(θ)=1+cosθ (polar coordinates) and I figured I'd try to do it in one integral from 0 to 2Pi. Homework Equations So the integral is \int_{0}^{2\pi} \sqrt{r^2 + (\frac{dr}{d\theta})^2}d\theta The Attempt at a...
  26. S

    Was Joan of Arc's Rise to Power Divine, Strategic, or Purely Legendary?

    According to my newspaper, today is the traditional date of the birthday of Joan of Arc in 1412. It's generally accepted she was born in that year but the birthdate may have been chosen because today is a feast day in both the Roman and Orthodox Catholic Churches (The Epiphany). Many of the...
  27. L

    Determine the lenght of arc and the area of the sector subtended by an

    Determine the length of arc and the area of the sector subtended by an angle of 60° in circle of radius 3 m Ok First change 60to radian measure. 60 x pi / 180° = 2pi / 6 Then.. I used the formula s = rθ 3(2pi/6) = 6pi/6 = pi <--- Is this right?? And how can I find the area which...
  28. S

    Understanding Simplification of Arc Length Calculations

    Homework Statement This is probably very simple, but I'm teaching myself arc length via Paul's Online Calculus Notes and there's a simplification on the page: I was wondering why the first Δx^2 was simplified to 1? I understand the other Δx^2 came out of the square root.
  29. D

    Can an Arduino and PWM circuit be used to create an arc generator and speaker?

    Hello everyone. My first post so bear with me. I'm planning on buliding an arcgenerator (and possibly an arc speaker later on if this works) with my arduino and a coil. I'm relatively to electrical engineering, so there are a few things I need some help with. If I've understood things...
  30. Z

    Variational Calculus - Minimal Arc lenght for given surface

    Homework Statement A curve is enclosing constant area P. By means of variational calculus show, that the curve with minimal arc length is a circle,Homework Equations The Attempt at a Solution F(t)= \int_{x_{1}}^{x_{2}}\sqrt{1+(f^{'})^{2}}dt G(t)= \int_{x_{1}}^{x_{2}}f(t)=const If i use...
  31. C

    What can I do with a CENCO High Pressure Mercury Arc Lamp ?

    What can I do with a "CENCO High Pressure Mercury Arc Lamp"? I'm a high school physics teacher. I inherited a "CENCO High Pressure Mercury Arc Lamp." Are there any useful demos and/or labs I can use this for?
  32. C

    Arc Formation in Jacobs Ladders

    When we see an arc between a Jacobs ladder is this because a charge density builds up between the rods and then the E field between the rods is strong enough to rip electrons off the molecules in the air and the start to conduct.
  33. S

    How to calculate arc length in unit circle

    http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg What is the method of calculating arc length in In the image above . x & y is known Thanks .
  34. B

    Arc Length Problem Find 0 ≤ x ≤ 3

    Homework Statement Find the arc length of y=x*e^(x^6) where 0 ≤ x ≤ 3 Homework Equations The Attempt at a Solution I took the derivative of the equation and squared it to get (e^2(x^6))(1+12(x^6)+36(x^12)) then plugged it into the proper formula to get: 3...
  35. Evil Bunny

    Can You Create an Arc in a Vacuum?

    Can you create an arc in a vaccum?
  36. D

    What is the equation for the center of mass of an arc?

    Homework Statement In the 1968 Olympic Games, University of Oregon jumper Dick Fosbury introduced a new technique of high jumping called the "Fosbury flop." It contributed to raising the world record by about 30 cm and is presently used by nearly every world-class jumper. In this technique...
  37. G

    Traversing a Circular Arc: Solving for Time with Maximum Acceleration

    Homework Statement A car is tested along specifically designed track. First, the car is driven along a straight section of track of length (r). If the car starts from rest under a maximum (constant) acceleration, it takes an amount of time (t) to cover the distance (r). The car is then brought...
  38. G

    Time to traverse a circular arc?

    Homework Statement A car is driven along straight section of track length (r). The car started from rest and the time it took to cover r distance is (t). If the same car is then tested on a circular arc of radius r, starting from rest and continues to speed up at the maximum possible rate that...
  39. P

    Charge Distrubution evenly on Arc (Radius R)

    Homework Statement A charge Q is distributed evenly on a wire bent into an arc of radius R, as shown in the figure below.What is the mathematical expression that describes the electric field at the center of the arc (point P indicated) as a function of the angle θ? Sketch a graph of the...
  40. ElijahRockers

    Unit Tangent Vector of a curve / Arc Length

    Homework Statement Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. Homework Equations r(t) = (-3tcost)i + (3tsint)j + (2\sqrt{2})t(3/2)k 0 ≤ t ≤ ∏ The Attempt at a Solution So I found dr/dt (I think), which is v(t) =...
  41. M

    Finding circle center from two points and an arc length

    I'm trying to find the equation for a circle given two points in x, y and the starting angle, arc length, and two points along the circle. I need to find the equation because I need to translate a sprite along the curved path from one point to another. The situation ends up looking like this:A...
  42. H

    How to use arc tan to find an angle?

    in physics we were doing a problem that essentially involved vectors and in the end we were left with 2 displacements. how would i find the angle between them if it was not a right triangle? i asked someone and they said that i could find it using artan(Ry/Rx) ...R being one of the displacements
  43. L

    Reparametrization to find arc length

    Homework Statement Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t. r(t) = [e^(2t)cos(2t)]i+2j+[e^(2t)sin(2t)]k Homework Equations i know that the derivative of the arc length with respect to t = magnitude of...
  44. L

    Arc welding plant power cut off

    I have an arc welding plant and I realized that I am wasting energy when it is not used but powered on. Can anyone please suggest a way to get rid of this problem? That is, plant gets "active" when it is welding and is "idling" when it is not welding.
  45. M

    How do I Integrate \sqrt{1+x^4+2x^2}?

    Homework Statement y=\frac{1}{3}\left(x^2+2\right)^{3/2} Homework Equations \int_{a}^{b}\sqrt{1+\left(\frac{dy}{dx}\right)^{2}}dx The Attempt at a Solution \frac{dy}{dx}=x\sqrt{x^2+2} \int_{0}^{3}\sqrt{1+\left(x\sqrt{x^2+2}\right)^{2}}dx=\int_{0}^{3}\sqrt{1+x^4+2x^2}dx I'm stuck...
  46. Philosophaie

    Trig function of arc trig functions and the reverse

    I know the sin(arccos(x)) = (1-x^2)^0.5 I was wondering what some of the others are: cos(arcsin(X)) tan(arcsin(X)) tan(arccos(x)) sin(arctan(x)) cos(arctan(x)) also the reverse: arcsin(cos(x)) arcsin(tan(X)) arccos(Sin(X)) arccos(tan(X)) arctan(sin(X)) arctan(cos(X))
  47. P

    Why Do High Energy Discharges Arc?

    I'm interested in understanding why high energy discharges arc rather than just travel in a more direct straight path. Thanks for the enlightenment.
  48. L

    Collimating Light from a Hg Arc Lamp

    Hi, I am trying to collimate light from a mercury arc lamp. I know this question has been asked before here https://www.physicsforums.com/showthread.php?t=413437&highlight=collimation but it was first posted last year and since my situation is a bit different it didn't quite answer all of my...
  49. E

    Derivation of Integral Arc Length Formula

    Homework Statement My textbook [Engineering Mathematics, Stroud, 6th Edition, page932] runs through the derivation of the integral formula for arc length. I got confused at one of the steps: [partial](ds/dx)=sqrt(1+([partial](dy/dx))^2) if [partial]dx tends to 0...
  50. F

    How Do Formulas for Sector Area and Arc Length Relate?

    I'm just wondering because I'm really confused right now. My teacher gave us the formula: K= \frac{1}{2}sr for area of a given sector where "s" is the arc length and "r" is the given radius. the formula for the arc length is: s=\Theta r Though, I can't seem to understand how he came up...
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