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

    Uniformly charged rod in an arc

    If a rod with charge density lambda is bent into a 3/4 circle what is the E field at the center? Well if the rod is 3/4 of a circle then neither the x or y components can cancel out, thus E= k*lambda/ R (i) + k*lambda/R (j) right?
  2. M

    Arc length in polar form θ = f (r)

    hi! i need some help here, do you have any available example on how to find the arc length in polar form θ = f (r)? using integral calculus, i mean. i searched the internet but i only got the r= f(θ) example. i hope you can help me. thanks!:)
  3. L

    Arc length and angle between two cities

    Two cities on the surface of the Earth are represented by position vectors that connect the location of each city to the centre of the earth. Assuming that the centre of the Earth is assigned the coordinates of the origin, and that the Earth is a perfect sphere, outline the steps that would lead...
  4. R

    Understanding Arc Length and Line Integrals for Surface Area Calculation

    Hello, I am trying to solve for the surface area of a odd surface for a fire relief PSV and needed to do a line integral but I was reading into my calculus book and going back to the definition of arc length I am confused: L = lim_{n\rightarrow\infty}\sum (P_{i-1}*P_{i}) Multiplication should...
  5. H

    Discover the Arc Tan Sum Formula for Math Help in Just a Few Steps

    Homework Statement Find the sum Arc(tan1/2)+Arc(Tan1/8)+...+Arc(Tan1/2*n^2) Homework Equations nothing The Attempt at a Solution
  6. S

    How do I solve for arc length?

    How do I solve this ?
  7. B

    Electric field of a charged arc

    Homework Statement A charge of 18 nC is uniformly distributed along a straight rod of length 4.7 m that is bent into a circular arc with a radius of 2.4 m. What is the magnitude of the electric field at the center of curvature of the arc? Homework Equations E=KQ/R^2The Attempt at a Solution...
  8. L

    Arc length/ surface area with integrals

    I have a question on the formulas for arc length and surface area. Do you use the formula: s= \int_{c}^{d}\sqrt{1+[g'(y)]^2}dy only when you are provided with a function x=g(y)?? Can you convert that to y=g(x) and solve it by replacing g'(y) with y(x), changing the bounds and the dy to dx...
  9. M

    Definition of arc length on manifolds without parametrization

    Curves are functions from an interval of the real numbers to a differentiable manifold. Given a metric on the manifold, arc length is a property of the image of the curves, not of the curves itself. In other word, it is independent of the parametrization of the curve. In the case of the...
  10. P

    Witnessing Electric Arc Furnace Melting Metal with Programming

    good day, this place is great, and i just got questions an AC electric arc furnace melts metal by way three electrodes and electric arcs generated by potential differences inside the furnace i had the opportunity to watch one in action and understanding the programming i see it controls...
  11. Peeter

    Newie relativity question: proper time vs. arc length?

    Doran/Lasenby define a proper interval as: \delta \tau = \int \sqrt{\frac{dx}{d\lambda} \cdot \frac{dx}{d\lambda}} d\lambda (c=1, x= (t,x1,x2,x3) is a spacetime event, and the dot product has a +,-,-,- signature) and say that this is called the proper time. I can see that this...
  12. Z

    Arc Length Need Verification, If Wrong, Can You Help?

    Homework Statement Length of curve: y=1/2(ex-e-x) from 0 to 2 Homework Equations s = ∫√[1+(dy/dx)^2] dx The Attempt at a Solution [sqrt(4+2e^(-x)+e^x)]*[-1+e^x]/[1+e^x]. = 3.323971
  13. T

    Volts/amps for an electric arc between points

    Can someone help me find these calculations or give me a point in the right directions? If I have a hollow insulating cylinder (has a diameter of 5 cm and a length of 14 cm) with two (conductive) sharp metal point contacts at each end (measuring 2cm each leaving 10 cm exactly between the...
  14. T

    How many volts/amps for an electric arc between points?

    Can someone help me find these calculations or give me a point in the right directions? If I have a hollow insulating cylinder (has a diameter of 5 cm and a length of 14 cm) with two (conductive) sharp metal point contacts at each end (measuring 2cm each leaving 10 cm exactly between the...
  15. H

    Simplifying a arc length problem

    Simplifying an arc length problem I have L= Int(-2..2) sqrt(16*cosh(4*t)^2+9*sinh(4*t)^2+9) and can use Maple to simplify this to sqrt(25*cosh(4*t)^2) but I just can't see how that is done. (or how to get maple to show me the steps!) Can anyone help by showing the steps, including any...
  16. L

    When I see an electrical arc ,what am I really seeing?

    When an electrical arc occurs, is the blue/white/purple arc the electricity itself, or is it a result of the electricity interacting with something in the air?
  17. J

    Why Does Changing Integration Limits Affect Arc Length Calculation?

    Homework Statement Find the length pf the curve over the given interval. r=1+\sin\theta 0\preceq\theta\preceq\2\pi The Attempt at a Solution Ok I set it up as: 2\pi \int\sqrt((1+\sin\theta)^2+cos^2\theta) 0 and by simplifying and integrating, I get...
  18. A

    Why does a rainbow form an arc shape?

    We all know as to why we see a rainbow. But why do we see it in a the form a circular arc. Why not a straight line or anything else? I was reading one book and that gave some reason that eyes make the a particular angle at the light from the drops of water. We all know the first part that we...
  19. D

    Calculating Polar Arc Length for r=1/theta from 2 Pi to Infinity | Homework Help

    Homework Statement Find the length of the spiral of r=1/theta for theta\geq2 \pi Homework Equations \int\sqrt{r^{2}+r'^{2}} The Attempt at a Solution I thought of the formula for polar arc length, which is the integral of the square root of the sum of the square of r and the square...
  20. M

    What I am doing wrong? arc length of parametric functions

    So this seems to be a pretty straightforward question but I keep getting the arc length to be 0 and I redid this question many times.. Find the length of the parametrized curve given by x(t) =t^{2}-8t + 24 y(t) =t^{2}-8t -7 How many units of distance are covered by the point P(t)...
  21. R

    Arc length of vector-valued function; am I starting right?

    Homework Statement Given: R(t)= <(1/2)t^2, (4/3)t^(3/2), 2*sqrt(3)t> Find: Arc length function s(t) where t_0 =0 Homework Equations Is this the correct formula? ∫[0,t] sqrt( derivative^2 + derivative^2 +derivative^2) dt ∫[0,t] sqrt(t^2 + 4t + 12) dt The Attempt at a Solution...
  22. R

    Arc length help extended to surface area and centroid.

    Homework Statement A curce,C, has equation y=x^{\frac{1}{2}}-\frac{1}{3}x^{\frac{3}{2}}+\lambda where \lambda>0 and 0\leq x \leq 3 The length of C is denoted by s. Show that s=2\sqrt{3} The area of the surface generated when C is rotated through one revolution about the x-axis is denoted...
  23. R

    Finding Arc Length of y=x^{\frac{1}{2}}- \frac{1}{3}x^{\frac{3}{2}}+\lambda

    1.Homework Statement y=x^{\frac}{1}{2}}- \frac{1}{3}x^{\frac{3}{2}}+\lambda For 0 \leq x \leq 3 Show that the arc length,s=2\sqrt{3} Homework Equations s=\int_{x_1} ^{x_2} \sqrt{1+ (\frac{dy}{dx})^2} dx The Attempt at a Solution \frac{dy}{dx}=\frac{1}{2\sqrt{x}} -...
  24. J

    Identifying Major or Minor Arc on a Circle: How Do Three Points Help?

    I have 3 points defined on an arc of a circle.I need to identify whether they lie on the major arc or minor arc.How is it possible? I know the three points. I know the radius of the circle
  25. T

    What is the electric field at the center of curvature of an arc?

    Homework Statement Determine the field at the center of curvature of an arc of arbitary angle \alpha (\alpha is with the x-axis) Homework Equations E=\frac{kQ}{R^2}\widehat{r} S=R\alpha \lambda=\frac{Q}{S} The Attempt at a Solution I divide the arc into small pieces ds...
  26. C

    How Do I Integrate the Last Part of This Arc Length Equation?

    I'm working on this problem x^5/6+1/(10x^3) [1,2] and I got the equation: sqrt(1+(5x^4/6-3/10^4)^2) or sqrt(1+25x^8/36+9/100x^8-1/2) I'm not sure how to integrate the last part, is there some sort of obvious substitution I'm missing?
  27. A

    How do I calculate the arc length of a polar curve?

    It's easy question,but I don't know whether I solved it correctly. Homework Statement Calculate the length of the curve given by r=a\sin^3 \frac{\theta}{3} in polar coordinates. Here, a > 0 is some number. Homework Equations l=\int \sqrt{r^2(\theta)+(\frac{dr}{d\theta})^2}d\theta...
  28. B

    Arc Length around Helical Torus

    Can anybody help? Mathematical Physics. I'm seeking an analytical expression for the path length of a point that follows a helical path with the helix wound about an axis to form a torus. The arc path length of a helix is simple to compute, but when its formed into a torus there is a...
  29. T

    Arc length trig vector problem

    I need help with this homework problem: Making a turn, a jetliner flies 2.1km on a circular path of radius 3.4km. Through what angle does it turn? Any ideas that would help me in doing it?? thanks
  30. J

    How can I simplify this derivative to make calculating arc length easier?

    Hi! Here's my question on finding arc length. If I've taken the derivative correctly, is there anyway I can simplify it before putting it into the arc length formula? Homework Statement Find the arc length where 0\leqx\leq2 y=(x^{3}/3)+x^{2}+x+1/(4x+4) Homework Equations...
  31. N

    Electric field due to arc of charge

    Homework Statement A circular arc of charge has a radius R and contains a total charge Q. If the angle of the arc is 90 degrees find: a) the charge density of the arc b) the electric field at point P in terms of the charge density L and the radius of the arc R L should really be lambda...
  32. N

    Second moment of area of a hollow cylindrical arc

    Homework Statement I need to find the second moment of area for a hollow cylindrical arc. When I searched the web, they had formulas for several shapes but I couldn't find this one The profile of my part is a little unusual as follows: R: Outer Radius = 35.089" r: Inner Radius = 35.050"...
  33. L

    How Do You Calculate the Arc Length of y=sqrt(x^3)?

    [SOLVED] Arc Length Problem y=\sqrt{x^{3}} So you plug it into the formula for arc length. (integral of the sqrt of 1+y'^2) And it yields \int \sqrt{1+(\frac{3x^{2}}{2\sqrt{x^{3}}})^{2}dx From there you would use trig substitution, 1+tan^2theta = sec^2theta. But converting the dx to...
  34. N

    Arc Length of an Ellipse: Formula & Calculation

    Is there a general formula for calculating the arc length between two points along an ellipse?
  35. M

    Arc Length Curve: Find Point at Distance 26pi

    Homework Statement Find the point on the curve r(t) = (5Sint)i + (5Cost)j + 12tk at a distance 26pi units along the curve from the point (0,5,0) in the direction of increasing arc length. Homework Equations L = int (|v|) from 0 to T. The Attempt at a Solution T comes to be 2pi...
  36. B

    Understanding Polar Coordinates and Arc Length Equations

    Homework Statement My book says if you write a plane curve in polar coordinates by p = p(?), a<=?<=b then the arc length is ??(p^2+(p')^2)d? (the integral is from a to b). It doesn't tell me how they got this equation though and I can't figure it out myself. what does the equation p(?) mean...
  37. M

    Angular Range of Motion for 2 Limit Sensors in 83° Arc

    If I have 2 limit sensors set in a circular arc around a rotating servo motor, and the angle between them is 83°, approximately what is the angular range of motion that I can achieve? Please take into account, and let me know what clearances I need to be aware of (i.e. how many degrees clearance...
  38. C

    How Can I Create a High Voltage Arc with Capacitors and Transformers?

    so I need to construct a device that creates a high voltage arc for an experiment, unfortunatly I don't know how to amplify the voltage without a series of transformers. I believe there is a way of doing this with a few capacitors, and right now I have about a dozen 12 MFD capacitors, and a...
  39. J

    Gas Molecules in an Electric Arc

    What exactly happens to the gas molecules in an electric arc? Oxygen turns to ozone, methane turns to acetelyene.
  40. V

    Joining two lines(3D) with a circular arc fillet

    Hi all, I have two lines in three dimensional form [P1(x1,y1,z1),P2(x2,y2,z2), and P3(x3,y3,z3), P4(x4,y4,z4) ] joined by a fillet, with known radius. i want to know the, start of the fillet(bend), end of the fillet, center of the fillet in a mathematical expression. with the above...
  41. B

    Car travelling around arc of circle

    This is not a homework problem, but a friend and I were discussing this and have not come to an agreement as yet. Supposing that we are in a car which is traveling a left curve in the road which is of constant radius, and we still have some way to go before the road becomes straight again...
  42. E

    Solving a Horizontal Arc HW Problem: Centripetal Acceleration

    Homework Statement A hawk flies in a horizontal arc of radius 13.5 m with a speed of 3.9 m/s. What is its centripetal acceleration? (I correctly found this to be 1.1267 m/s².) Next question is: If it continues to fly along the same horizontal arc but increases its speed at a rate of...
  43. C

    Arc Length and Smooth Curves: Understanding the Basis for Assumptions

    Guys, I need your kind assistance. I am studying arcs length. Suppose a vectorial function with domain [a, b] (interval in R) and range in RxR. This range is a curve in the RxR plane. Take a partition P of [a, b]: a= t0, t1, t2,..., tn = b. We have a straight line which goes from F(t0) to...
  44. M

    What is the weight of a cable hanging between two poles?

    Homework Statement A cable hangs between two poles of equal height and 39 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x)=10 +(0.4)( x^{1.5}) The cable weighs 12.5...
  45. P

    Using integrals to calculate arc length

    Homework Statement Just started Calc II last month, it's been smooth so far but I've run into a bit of snag involving the application of integrals in the calculation of arc length. The formula you use is the definite integral of (1+(d/dx)^2)^.5. Often once you derive the d/dx and...
  46. S

    Limits of Arc Tangent (a) and (b)

    Homework Statement Evalute: a) lim (x->0) (arctan x)/x b) lim (x->1) (arctan(x) - pi/4)/(x-1) Homework Equations Inverse tangent, trig identities. Kline's calculus, which I am teaching myself from, does not have that much detail on limits. The Attempt at a Solution For (a), I...
  47. F

    Minimum Voltage and Current for Electric Arc at One Inch Distance

    What would be the minimum direct or alternating voltage and current needed to produce an electric arc in air at a distance of one inch ?
  48. S

    What is the surface area when rotating a curve about the x-axis?

    1 Find the area bounded by the curve x = t - \frac{1}{t} , y = t + \frac{1}{t} and the line y = 2.5 . I know that A = \int_{\alpha}^{\beta} g(t)f'(t) \; dt I ended up with \int_{1}^{2} 2.5-(t+\frac{1}{t})(1+\frac{1}{t^{2}}) 2 Find the length of the curve: x = a(\cos \theta + \theta...
  49. W

    Why is the Absolute Value of X Taken in the Derivative of Arc Secant?

    Hello there In the derivative of the arc secant, why is the absolute value of x ( which is present in the denominator) taken? Is this to prevent the possible of having a zero ( and making the whole expression undefined ? ) Thanks
  50. C

    Electric potential at center of circular arc

    An insulating rod of length l is bent into a circular arc of radius R that subtends an angle theta from the center of the circle. The rod has a charge Q ditributed uniformly along its length. Find the electric potential at the center of the circular arc. Struggling with this problem. I...
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