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. C

    12 volt generation of a sustained arc

    I need help finding a device that can generate a sustained arc while utilizing only a 12 volt power source. Does anyone have any ideas? Arc should be able to jump a 1 and a half inch gap. Also what materials should I use for the electrodes that would not degrade over time?
  2. H

    Velovity of a light beam in an arc

    I was using a small penlight laser around the floor to have my cat chase the impossible dot. A though came that if I could move the dot fast enough from my porch , and with sufficient power, that at some distance along an arc the dot would move faster than the speed of light. Any comments...
  3. R

    Approximating arc length of Bezier by another Bezier

    (Note: cross posted to http://www.devmaster.net/forums/showthread.php?t=16227 ) Hey everyone, As we know, the arc length of a cubic Bezier spline is kinda hard to calculate. There's no closed-form mathematical expression, so most people just subdivide it into a bunch of line segments and...
  4. Saladsamurai

    When is arc length ≈ chord length

    Homework Statement Maybe this is precalculus? Either way, here is a question that I am curious about. Take a circle of radius R and sweep out an arc length SAB with endpoints 'A' and 'B' over angle theta. For a short enough arc length, I believe that we could approximate SAB by the chord...
  5. C

    Calculating Arc Length for f(x) = 4/5*X^5/4 from [0,4]: Step-by-Step Guide

    I need to find the arc length of the function f(x) = 4/5*X5/4 from [0,4]. You have to find f '(x) first and that would be X1/4 I square f '(x) and obtain X1/2 or \sqrt{X} I plug it into the formula and get S = \int\sqrt{1+\sqrt{X}} from [0,4] I don't know how to evaluate the...
  6. S

    How to measure the temperature of an arc discharge

    Hi all, I was thinking about measuring the temperature of an arc discharge. The size of the discharge is very small, in the order of micrometer. So it is not possible to put a thermocouple near the it. Thank you very much.
  7. K

    How Do You Find an Arc Length Parametrization for a Given Curve?

    Homework Statement Find an arc length parametrization of the curve r(t) = <e^t(cos t), -e^t(sin t)>, 0 =< t =< pi/2, which has the same orientation and has r(0) as a reference point. Homework Equations s = int[0,t] (||r'(t)||) The Attempt at a Solution So I found the derivative of r(t), and...
  8. R

    What is the relationship between club length and club speed in a golf swing?

    Hi everyone, I started what I thought would be a simple algebra/trig problem and quickly learned that I was dead wrong. At least I think I am wrong. I need to determine how much the speed of a particle moving along an arc segment changes as the length of the distance to the center point...
  9. I

    Radius of an Arc Inside an Arc

    Homework Statement Say there are two arcs which are part of the circumference of a circle within a circle with the same angles, but since one arc belongs to the circle outside, that arc is longer than the arc inside it. If the first arc has length s, then the second arc has length s + \Delta s...
  10. C

    Xe Arc Lamp Safety: IR NIR Risk Analysis

    Hey all, When it comes to arc lamps, it looks like the safety concern everybody talks about is in regards to UV exposure. This, however, seems to be more suited for Hg sources instead for Xe sources. My question is in regards to whether there should be any concerns with the IR portion of the...
  11. S

    How Do You Calculate the Length of a Cardioid in the First Quadrant?

    Homework Statement Find the length of the cardioid with equation r = 1 + cos (theta) located in the first quadrant Homework Equations f (theta) = 1 + cos (theta) f'(theta) = -sin (theta) s = antiderivative (0 to (pi/2)) sq rt (f(theta)^(2) + f'(theta)^(2)) d(theta) The Attempt at...
  12. S

    Calculating Arc Length for Polar Curve r = theta^(2)

    Homework Statement Find the length of r = theta^(2) for 0<=theta<=pi Homework Equations Arc length s = antiderivative of sq rt (f (theta)^(2) + f (derivative theta)^(2)) The Attempt at a Solution I have worked my way to the antiderivative of sq rt (theta^(4) + 4(theta)^(2)) but I'm...
  13. P

    Arc Length in Polar Coordinates

    In the polar formula for arc length, ds^{2}=dr^{2}+r^{2}d{\theta}^{2}, what is the exact meaning of the r^2 term multiplying d{\theta}^2? Is it an initial distance from the origin? A final distance from the origin? The change in r from point a to point b? This baffles me to no end and nothing...
  14. H

    Arc length of vector function curve

    Homework Statement 1. Find the length of the curve from t=0 to t=1. r(t) = <2t, t^2, (1/3)t^3> 2. 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)cos2t, 2, e^(2t)sin2t>Homework Equations S = \int{r'(t)} dt...
  15. K

    Concept: Arc Length Parametrization

    What does the arc length parametrization mean?
  16. B

    Find the arc length of f(x) (x^(5/4))/5

    Homework Statement find the arc length of f(x) (x^(5/4))/5. The integration limits are from 0 to 4. Homework Equations The arc length formula is integrate sqrt(1 + (f'(x))^2) The Attempt at a Solution f'(x) = (5/4)*(1/5)*x^(1/4) = x^(1/4)/4 integral of sqrt(1 +...
  17. A

    What is the magnitude of the magnetic field at the center of the arc?

    A current I = 3 A flows through a wire perpendicular to the paper and towards the reader at A and back in the opposite direction at C. Consider the wires below the plane at A and C to be semi-infinite. In the figure, L1 = 3 m, R = 6 m, and L2 = 6 m and there is a B = 2.37 T magnetic field into...
  18. mnb96

    Shortest arc between two points in polar coordinates

    Hello, If we consider a Euclidean plane \mathbb{R}^2 with the ordinary inner product, and we "distort" it through a cartesian->polar transformation, how should I compute the shortest arc between two points (r,\theta) and (r',\theta') ?
  19. J

    Sketching y=cos-1(2x) and y=sin-1(3x): Guide

    Homework Statement Sketch y = cos-1(2x) and y = sin-1(3x) Homework Equations The Attempt at a Solution This is my attempt cos-1(2x) = y, which means cos y = 2x produce a table with y from (-pi/2 to pi/2) What I want to confirm is the 2x. I need do 1/2 x instead of 2x when...
  20. J

    How can the length of a cardioid be calculated using polar coordinates?

    Homework Statement Find the total length of the cardioid r=a(1-cos theta) Homework Equations ds2=r2dtheta2+dr2 ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta The Attempt at a Solution dr=a(sin theta)d theta ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d...
  21. S

    Polar Regions: Area, Arc Length, and Surface Area

    Homework Statement Consider the graph (see attachment) of r = 1 +2cos\Theta in polar coordinates. SET UP integrals to find 1. the area inside the large loop minus the area of the small loop. 2. the arc length of the small loop 3. the surface area of the surface formed by...
  22. L

    Is It Possible To Shape An Electric/Plasma Arc?

    I was watching the visualizer while listening to a song in winamp, and this particular one has two speakers that shoot sine waves. I was watching it and I thought to my self: "it would be great if I reproduce that in real life". After thinking about it my thoughts went to back to that arc...
  23. L

    Plasma Arc Speaker: How Does It Work?

    I saw THIS video and THIS OTHER ONE I was really quite surprised that such a thing was actually made to work. I'm curious how one could create an arc such as that, and then modulate it to match an audio signal. From my interpretation the extreme voltage causes an arc between the contacts...
  24. A

    Solving Arc Tangent Squared: tan(2x) - 3cot(2x) = 0

    Homework Statement tan(2x) - 3 cot (2x) = 0 Homework Equations Trigonometry Knowledge. The Attempt at a Solution tan(2x) - 3cot(2x) = 0 tan(2x) - 3/tan(2x) = 0 [tan(2x)]^2 - 3 = 0 [tan(2x)]^2 = 3 Is there such thing as Arc Tangent that's squared??
  25. L

    Area, Arc Length, Volume & Curved Area of y=√x

    Homework Statement For the curve y=\sqrt{x} , between x = 0and x = 2, find (a) the area under the curve, (b) the arc length, (c) the volume of the solid generated when the area is revolved about the x axis, (d) the curved area of this solid. Homework Equations ds = \sqrt {1+(y')^{2}}dx...
  26. J

    Finding the Arc Length of a Polar Function

    Hi, I've been having some issues in solving this problem. Homework Statement Find the arc length of r=2/(1-cosθ) from π/2 to πHomework Equations L =(integrate) sqrt(r2+(dr/dθ)2)dθ The Attempt at a Solution I found (dr/dθ) = (-2sinθ)/(1-cosθ)2 so (dr/dθ)2 = (4sin2θ)/(1-cosθ)4 Then r2 =...
  27. M

    Calculating Variable Pulling Force on a Spring on an Arc

    Homework Statement As test of strength, a diabolical trainer sets up the following apparatus. The trainee must maintain a variable pulling force which is always tangent to a nearly frictionless, semicircular surface . By slowly varying the force, a block with mass 23.0 kg is moved (at a very...
  28. R

    Define Circle Knowing Two Points and ARC LENGTH Only.

    I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I...
  29. K

    Finding Arc Length when given velocity and launch angle

    Homework Statement Find the arc length of the projectile from launch until the time it hits the ground, given that 0 V is 100 feet/sec and is 45 degrees. Homework Equations Arc Length= ∫_a^b▒√(█(1+(f^' (x) )^2@)) dx Arc Length of Curve= ∫_a^b▒〖v(t)dt=∫_a^b▒√((dx/dt)^2+(dy/dt) )〗^2...
  30. R

    Solving for arc length of an ellipse

    Homework Statement The task is to solve for the arc length of an ellipse numerically. a & b are given for an ellipse centered at the origin and a value for x is given. Homework Equations Equation of ellipse is given to be x^{2}/a^{2} + y^{2}/b^{2} = 1 and the equation to solve for the arc...
  31. O

    Arc Length of e^5x from 0 to ln(4)

    Homework Statement http://i47.tinypic.com/1z6naa.jpg Note... I used wolfram alpha to get the answer, I did not get it myself... So I still need help. The answer shown is correct, so you'll know if you got it. Homework Equations Integral [0, ln(4)] sqrt(1+(dy/dx)^2) The Attempt at a...
  32. 3

    Solving Arc Length Problem: y=x^5/6+1/10x^3, 1≤x≤2

    Homework Statement Find the arc length of the curve: y=\frac{x^5}{6}+\frac{1}{10x^3} 1\leqx\leq2 Homework Equations ds=\sqrt{dx^2+dy^2} ds=\sqrt{1+\frac{dy}{dx}^2}dx The Attempt at a Solution \frac{dy}{dx}=\frac{5}{6}x^4-\frac{3}{10x^4}...
  33. S

    Arc length: Can't Solve the Integral

    Find the exact length of the curve analytically by antidifferentiation: y = (x3/3) + x2 + x + (1/(4x +4)) on the interval 0 < x < 2So I set it up using the length of a curve formula: L = \int\sqrt{1+(x^2+2x+1+(\frac{-1}{4(x+1)^2}} And simplified it to L =...
  34. M

    Arc Length of y=ln((e^(x)+1)/(e^(x)-1))

    Arc length of y=ln((e^(x)+1)/(e^(x)-1)) on [a,b] Using L=\int\sqrt{1+(y')^2}dx on [a,b] I am having difficulties differentiating y and plugging the results back into get a useful integral. So far I have y'=2e^(x)/(e^(2x)-1)
  35. Y

    Calc III Problem Integrating Sq Rt's in Arc Length Formula

    Hey guys, I'm studying for a test in calc 3 tomorrow and have run into a problem. On the practice test we have a problem "Find the length of the curve: r=theta^2, 0≤theta≤pi/2" I know the length of a curve in polar coordinates is int(sqrt(r^2 + (dr/dtheta)^2))dtheta...but when I get to where...
  36. B

    Calculate Arc Circle Volume: Step-by-Step Guide

    Homework Statement Trying to either derive or find a formula for the volume given by the space carved out from the area between an arc and the center of a circle. Essentially, the area between an arc and the center of a circle rotated 360 degrees, almost a cone shape with the upper boundary...
  37. C

    Line integral with respect to arc length

    In a line integral with respect to arc length, we have something like f(x, y)ds "inside" the integral sign. The ds tells us that we are working with the arc length function s, taking diferences (s_K+1 - s_k) in the sums that tend to the line integral. Question: do we shall understand that...
  38. C

    When we use arc length as a parameter

    If we have a fly in a room, its position respect to some frame of reference will change with time, so if we want to describe the fly's movement with a parametrized curve, it is easy to see the convenience of taking time as the parameter. I read that we can also take the length of the curve as...
  39. Char. Limit

    Arc Length Confusion: What is the Idea Behind it?

    Why is arc length of a function f(x) from a to b defined as \int_a^b \sqrt{1+(f'(x))^2} dx? Where they get the idea of squaring the derivative, adding 1, taking the square root, and then integrating it is beyond me.
  40. L

    Topological Definition of Arc Length

    In calculus, the definition of the arc length of some curve C is the limit of the sum of the lengths of finitely many line segments which approximate C. This is a perfectly valid approach to calculating arc length and obviously it will allow you calculate correctly the length of any...
  41. T

    What Is the Explosion Radius in a Worst-Case LOX and LIN Scenario?

    OK all since I do not have a physics background I figured I would come to the WWW and search those who did. I am needing some questions answered... here is the badckground info...I work and a Cryogenic plant that has a max of 17000 gallons of Liquid Oxygen and 12000 of liquid nitriogen on hand...
  42. O

    How do i find the arc length of an implicit curve given by f[x,y]=0?

    ? i used the implicit function theorem to find dy/dx, then applied that to the arc length formula, but i have to integrate with respect to x and there is the implicit function y[x] inside the radical. also, if it matters, the curve is assumed to be closed.
  43. D

    Calculate the change in the arc

    please help urgent! in the following question, E=65 GPa V=0.3 find the new length of the arc BD?? i have found the stresses xx=-56Mpa yy=0 xy=-28Mpa using hookes law i can find the strains xx=-8.615e-5 yy=2.58e-4 0.5*xy==-1.12e-3 but how do i calculate the...
  44. T

    Electric field at the center of an arc

    Homework Statement A charge Q is arranged evenly on a wire bent into an arc or radius R as shown in the Figure. What is the electric field at the center of the arc as a function of the opening angle theta? Sketch a graph of the electric field as a function of theta for 0<theta<180 degrees...
  45. D

    Calculating Length of Arc BD with Hookes Law

    in the following question, E=65 GPa V=0.3 find the new length of the arc BD?? i have found the stresses \sigmaxx=-56Mpa \sigmayy=0 \sigmaxy=-28Mpa using hookes law i can find the strains \epsilonxx=-8.615e-5 \epsilonyy=2.58e-4 0.5*\epsilonxy=\gamma=-1.12e-3 but how do i calculate the...
  46. S

    Arc length of vector function with trigonometric components

    Homework Statement Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case. r(t) = (c2/a)cos3t i + (c2/b)sin3t j where i and j are the usual unit vectors, 0 \leq t \leq 2\pi, c2 = a2 - b2, and 0...
  47. F

    Why did the multimeter leads arc?

    I was about to go out to the car to check how many amps were being drawn from a parasitic component in the circuit. Battery has been dieing if I leave it connected for a few days. The 12VDC test light connected from the positive battery post to the positive cable(after pulling cable off) shows...
  48. C

    Is this a reliable way to measure an arc

    I have a brass rod with a 90 degree bend. I want to measure the outer and inner radii by placing a piece of string along both of them, and then straightening the string out to determine the linear measurement. Is this an accurate method?
  49. P

    Why rainbow has a shape of arc and why its ends are bent down.

    why rainbow has a shape of arc and why its "ends" are bent down. Can anyone explain why rainbow has a shape of arc and why its "ends" are bent down.
  50. 2

    Arc Length Problem: Find s & Deduce y=e-s | Oscar

    Hey guys, Got a bit of a problem with a question I found in a textbook. I can do most of it but there's one little part I'm really struggling with: A curve C is given parametrically by: x=t-tanht, y=secht, t\geq0 The length of arc C measured from the point (0,1) to a general point...
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