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. S

    Can an electric arc cause a combustion or fire if

    Can an electric arc(such as this one http://upload.wikimedia.org/wikipedia/commons/7/7a/Electric_arc.jpg ) cause a combustion or fire if a 91 percent alcohol solution is sprayed on it?Thanks
  2. Z

    MHB How to Calculate Arc Length for a 124° Angle in a Circle?

    A circle has a radius of 10cm. Find the length s of the arc intercepted by a central angle of 124° . Do not round any intermediate computations, and round your answer to the nearest tenth. How do I do this?
  3. B

    Continuity of an arc in the complex plane

    Hello everyone, I have a rather simple question. I have the curve ## C(t) = \begin{cases} 1 + it & \text{if}~ 0 \le t \le 2 \\ (t-1) + 2i & \text{if }~ 2 \le t \le 3 \end{cases} ## which is obviously formed from the two curves. This curve is regarded as an arc if the functions ##x(t)## and...
  4. ArcanaNoir

    Arc length of intersecting circles

    Homework Statement My class is working through chapter 2 of Newman's Analytic Number Theory text (on partitions). We have come to a part where he states that "elementary geometry gives the formula" (for the length of arc A) 4r\text{arcsin}\frac{\sqrt(2)(1-r)}{\sqrt(r)} We are attempting to...
  5. Hijaz Aslam

    Electric Field of a circular arc at a point

    Homework Statement Given that the circular arc wire with radius 'r' has a linear charge density ##\lambda##. What is the Electric field at the origin? Homework Equations ##\vec{E}=\frac{kq}{r^2}## where ##k=9\times10^9## is a constant. 3. The Attempt at a Solution I took a small segment dy...
  6. admbmb

    Conceptual trouble with derivatives with respect to Arc Length

    Hi, So I'm working through a bunch of problems involving gradient vectors and derivatives to try to better understand it all, and one specific thing is giving me trouble. I have a general function that defines a change in Temperature with respect to position (x,y). So for example, dT/dt would...
  7. A

    Find the arc length parametrization of a curve

    Homework Statement Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) . Homework Equations s(t)=integral of |r'(t)| dt The Attempt at a Solution I was able to get the integral of the magnitude of the velocity vector to simplify to: s(t) = integral of...
  8. E

    Determine center point of offset circle

    I am working on an algorithm which requires the coordinates for the center point of an offset circle. Dimensions available to find this are shown in the image below and the dimension required is labeled as X: The point at the very left of the arc is a quadrant therefore, the circle center also...
  9. S

    Question about circle arc length formula

    Now i haven't checked yet whether or not this is correct, but the formula for the length of an arc that subtends a central angle can also be expressed this way: AC/360 Where: A: Central Angle C: Circumference Is this correct? Thank you for your help.
  10. L

    Calculating Arc Length of a Curve: A Calculus II Problem

    Homework Statement Find the exact length of the curve: y= 1/4 x2-1/2 ln(x) where 1<=x<=2 Homework Equations Using the Length formula (Leibniz) given in my book, L=Int[a,b] sqrt(1+(dy/dx)2) I found derivative of f to be (x2-1)/2x does that look correct? The Attempt at a Solution I found f'...
  11. C

    Calculating Arc Length of a Curve: y^2 = x^3, (1,-1) to (1,1)

    Homework Statement A curve has the equation y2 = x3. Find the length of the arc joining (1, - 1) to (1, 1). Homework Equations The Attempt at a Solution I took the integral of the distance and tried to evaluate from -1 to 1. L = [intergral (-1 to 1) sqrt (1+(dy/dx x^3/23/2)2 dx] Evaluated I...
  12. C

    Find Arc Length of Particle Moving on Curve

    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. The equation is r(t) = a(cos t + t sin t)i + a(sin t - t Cos t)j, 0</=t</=2pi, a>0Homework Equations Arc length =...
  13. I

    MHB Interval for the Length of an Arc

    find the length of an arc of a helix r(t)=(sint,cost,t) from the point (0,2,0) to (0,5,2pi) would the interval when integrating be from 0 to 2pi because t in the case is (z=t)? please say yes. please say yes.
  14. I

    MHB Arc Length C: Origin to (6,18,36)

    let C be the curve of intersection of the parabolic cylinder $x^2=2y$ and the surface $3z=xy$. find the exact length of C from the origin to the point (6,18,36). please help! this is the last question i have left from this assignment and i have no idea how to do it. i have grading to do and a...
  15. S

    Polar Arc Length: Solve Integral of r=6cos6θ

    Homework Statement Find the arc length of one of the leaves of the polar curve r= 6 cos 6θ. Homework Equations L = ∫sqrt(r^2 + (dr/dθ)^2) dθ (I use twice that since the length from 0 to π/12 is only half the petal) The Attempt at a Solution I seem to get an integral that can't be...
  16. T

    Electric Field from Arc of Charge - Need Help

    Electric Field from Arc of Charge - NEED HELP WITHIN AN HOUR I have literally been working on this all day and I am finally turning it over to someone better at physics then myself. This is due within two hours and I'm starting to doubt my ability to finish this, any help will be beneficial...
  17. Shackleford

    What is the arc length parametrization of α(t) and why is the s so tiny?

    Of course, I need to find the first derivative and integrate its norm. α'(t) = (1, 0, (1/2)t^2 - (1/2)t^-2) ∫ [1 + (1/4)t^4 + (1/4)t^-4]^(1/2) dt, t = 1 to t = 3. Have I simply forgotten useful integrals? α'(t) = (e^t, -e^-t, root2) ∫ [e^2u + e^-2u + 2]^(1/2) du, u = 0 to u = t.
  18. R

    Understand the major arc connecting two points on a sphere

    I am not sure if this is the right forum for this question, but I arrived at the question while studying the principle of stationary action so here it is: Consider the problem of finding the shortest path between two non-antipodal points on a sphere. Usually one solves this by using calculus of...
  19. S

    MHB Arc Length and Rotation, Please Explain this problem

    EDIT: Okay now that the admin has cleaned up my mess, please scroll down to see the correct image and the question on the 3rd post in this thread.
  20. I

    MHB Find arc length starting from P_0

    find the arc length function for the curve $y=2x^{3/2}$ with starting point $P_{0}(1,2)$. how do i do this? this is what I've done so far. $y'=3\sqrt{x}$ $1+(3\sqrt{x})^2=9x+1$ $\int_{a}^{b} \ \sqrt{9x+1},dx$ what's my a and what's my b?
  21. I

    MHB Find Arc Length with TI-Nspire Calculator

    how do i use the nspire to find arc length?
  22. haruspex

    Shape and Position of a Descending Rope Over a Drum: A Surprising Solution

    This is a problem I thought up. If I'm correct as far as I've gone, the answer is rather surprising. A thin but 'massive' rope lies coiled on a floor. Treat the coil as a point. One end passes vertically up and over a smooth cylindrical drum radius r. The centre of the drum is height h...
  23. O

    Understanding Corona, Arc, and Spark in Fluids: Explained

    There are tons of different explanation for each of them in internet. Could someone please confrim the explanation below which I gathered from different places; If the electrical field in a fluid reaches the fluids dielectrical strenght, dielectric collapses and corona happens, but since the...
  24. F

    Is the Area Under a Curve Equal to its Arc Length?

    I learned in my calc 1 class that to calculate the arc length of a curve, we are to compute the integral of the function. For example, the integral of a function that describes the path of a thrown baseball would give the total distance traveled by the baseball (I hope I'm using the term arc...
  25. D

    Troublesome Arc Length Problem

    1.) The problem is: Find the arc length of f(x)= x^3/3-1/(4x) from x=1 to 2 2.) Relevant formulas: ds = √(1+(dy/dx)) abs(L) = ∫ds 3.) My work so far: f'(x)= x^2+1/(4x^2) abs(L) = ∫(from 1 to 2) √(1+(x^2+1/(4x^2))^2 dx = ∫(from 1 to 2) √(1+(x^4+1/2+1/(16x^4)) dx = ∫(from 1...
  26. T

    Solving Arc Problem with Given Values & Co-ordinates

    Hello all I was hoping someone could help me with a geometry problem. Firstly this is not a homework question – this is work related I am just not very good with Maths. I have been asked to set out an arc for a wall. I have been given all the values I need but I do not know how the...
  27. A

    Solving for Spiral Arc Length: A Scientist's Approach

    So here's a little background for the question: I have an arc that covers 3/4s of a circle (so it's not quite a full circumference) such that the radius from the center of the arc varies with respect to the angle (dR/d(theta)) (and it can be either positive or negative, but not constant). I am...
  28. N

    Difficult simplification for Arc length integral

    Homework Statement Find the length of the curve x = 3 y^{4/3}-\frac{3}{32}y^{2/3}, \quad -64\le y\le 64Homework Equations Integral for arc length (L): L = \int_a^b \sqrt{1 + (\frac{dy}{dx})^{2}} dx The Attempt at a Solution Using symmetry of the interval and the above integral for arc length...
  29. J

    Radius of circumference as function of arc lenght and height

    Homework Statement I don't know the radius of the circumference. I could only measure the arc lenght, and the height. I know the guidelines say we should not post images, but this is a geometric problem and I think it is something logic to show it with a picture. So the variables are the...
  30. C

    Find area of the region bounded by the circular arc in 1st Quadrant

    Homework Statement Find the area of the region in the first quadrant, which is bounded by the x-axis, the line x = 2 and the circular arc x^2 + y^2 = 8Homework Equations The Attempt at a Solution I didn't use the hint given in the question but does my answer still makes sense. Did I set up the...
  31. E

    Solving Arc Length Integral with Trigonometric Substitution

    ∫sqrt(x^4/4 + 1/(x^4) + 1/2) dx from x = 1 to 4 Could someone help me solve this? I can't seem to find a substitution that works, or find the square root of (x^4/4 + 1/(x^4). Any help would be very appreciated. Thanks in advance!
  32. S

    MHB Finding the arc length / length

    This may seem like a dumb question, but is finding the "arc length" of a curve and finding the "length" of a curve the same thing? Just worded differently?
  33. A

    Why is the center of mass assumed to be on the vertical in an arc?

    Homework Statement image attachment Homework Equations The Attempt at a Solution i have the solution , but in it , he assumes the center of mass is on the vertical and thus the distance of the vertical from the center is rsin(1/4∏)/(1/4∏) where r is the radius , so why did he...
  34. A

    Arc Length Units: Explained & Solved Problem

    Hello, I solved the arc length for a particular problem. However, what is the unit of arc length if the units of the velocity vs time graph are m/s vs s? I am really confused.
  35. Y

    Proof of Arc Length Parameter

    1. The problem statement, all variables and given/known If C is a smooth curve given by r(s)= x(s)i + y(s)j + z(s)k Where s is the arc length parameter. Then ||r'(s)|| = 1. My professor has stated that this is true for all cases the magnitude of r'(s) will always equal 1. But he wants me...
  36. S

    Finding arc length using integration

    Find the length of the positive arc of the curve y=cosh^{-1}(x) (for which y≥0) between x=1 and x=\sqrt{5}. My attempt: x=cosh(y) → \frac{dx}{dy} = sinh(y) → (\frac{dx}{dy})^{2}=sinh^{2}(y), so ds=dy\sqrt{1+sinh^{2}(y)}, therefore the arc length is S=\int_{y=0}^{y=cosh^{-1}(\sqrt{5})} cosh(y)...
  37. jmex

    How Can I Find KVA Rating and Power Factor Data for an Electric Arc Furnace?

    hello frnz i m aiming to provide a compensation scheme for electrical arc furnance but i don't have practical data to deal with.Is there anyone who could provide me rating of electric arc furnace (KVA rating n power factor).
  38. R

    MHB Find arc length given chord, radius

    The solution to this question (whose answer is pi) is eluding me: The radius of a circle is 3 feet. Find the approximate length of an arc of this circle, if the length of the chord of the arc is 3 feet also.
  39. A

    MHB Integration question (obtained from arc length question)

    how do i integrate the function sqrt(1 + 1/2(y^1/2 - y^(-1/2))^2) from 0 to 1??
  40. B

    What is the potential at point P at the center of this arc?

    Homework Statement What is the potential at point P due to a point charge Q at a distance R from P? Set V=0 at infinity. The same charge has been spread uniformly over a circular arc of radius R and central angle of 40 degrees. What is the potential at point P at the center of this arc...
  41. M

    Complicated Arc length problem

    Homework Statement The length L or the curve given by \frac{3y^{4}}{2}+\frac{1}{48y^{2}}-5 from y=1 to y=2 Homework Equations The Attempt at a Solution Setting up the formula is easy. First I found the derivative of f(y) which is: f'(y)=6y^{3}-\frac{1}{24y^{3}} Then I plugged...
  42. ThomasMagnus

    Relating Arc Length and Standing Wave Patterns

    Homework Statement I am currently reviewing the physics of 'standing waves on a string'. I know that for the nth harmonic, the length of the 'string' is \frac{n\lambda}{2}. Instead of just memorizing these, I have been trying to apply my knowledge of Calculus to figure out why these numbers...
  43. H

    Finding the length of an arc of a parabola

    Homework Statement y^2 = x from (0,0) to (1,1) Homework Equations L = ∫√(1+[g'(y)]^2) dy The Attempt at a Solution So this is a problem in my textbook that has been bothering me because I can't seem to come up with the same answer. 1. [bounds 0 to 1] 1/2∫ sec^3θ was obtained...
  44. K

    How to calculate a trapeze/ pendulum's arc distance

    Homework Statement This is an update to an earlier post. Since then, I now understand that a pendulum stops when its tension force= mg sin(theta)--because then centripetal force will=0, so velocity will be 0. However, now I am trying to determine how a trapeze would work on the moon. Homework...
  45. C

    Arcing - What affects size of arc when switch is opened?

    When an electrical circuit is opened or closed there is an arc between the terminals/buss that the switch or breaker is connecting or disconnecting and the arc is greater depending on the amount of voltage. My question is, is the arc greater when there is a resistance/load on the circuit? I'm...
  46. L

    Calc 2: Arc Length from 0-π/4 for James Stewart 7th Ed.

    Ello every one, i have interesting question. Any one who has james stewert 7th edition calc book I am on secotion 8.1 studying for an exam. number 13 of 8.1 says this y= ln(secx) find arc length from 0-pi/4 here is what i do first in my opinion. y`= 1/sec(sectan) y`= tanx...
  47. J

    Calculate the arc length of the vector function

    Homework Statement Calculate the arc length of <2t,t^2,lnt> from 1=<t=<e Homework Equations Arc length=∫√{(x')^2 + (y')^2 + (z')^2} The Attempt at a Solution So I have gotten to this point: ∫√{4 + 4t^2 + \frac{1}{t^2}} Am I on the right track, and if so, how do I integrate that?
  48. T

    Conservation of energy in a circle arc.

    http://www.natuurkunde.nl/servlet/supportBinaryFiles?referenceId=1&supportId=606217 Hello everyone, I was wondering if anyone could shed some light on the following problem: While composing a practise test for a chapter about conservation of energy, I made a problem like the one in the...
  49. C

    Arc length parametrisation question (error in notes?)

    This is from my course notes http://img28.imageshack.us/img28/2630/ckyl.jpg In line 3, there's the integral \int_0^t ||y'(s)||ds which represents the length of the curve as a function of t (which I am thinking of as time). Here, I think s is a dummy variable for time. The equation in line...
  50. PsychonautQQ

    Finding the Arc Length Parameterization of a Vector Function

    Homework Statement Find the arc length parameterization of r(t) = <(e^t)sin(t),(e^t)cos(t),10e^t>The Attempt at a Solution so I guess i'll start by taking the derivative of r(t)... r'(t) = <e^t*cos(t) + e^t*sin(t), -e^t*sin(t) + e^t*cos(t), 10e^t> ehh... now do I do ds = |r'(t)|dt and...
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