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Calculating the Electric field at a point due to a ring of charge

  1. Dec 23, 2013 #1
    I don't know if this is the correct section. It is not exactly a homework problem, but here it is:

    If I were given a circle of charge with radius r and were asked to find the electric field due to this circle of charge at the center of the circle, would it be valid to do the following:

    Since I know the radius of the circle of charge, could I imagine the circle of charge to be a line of charge, and the point in question be r away. That is, find the circumference of the circle, as if I were stretching out the circle into a straight line of length equal to the circumference of the circle. Then, I could calculate the electric field due to the line of charge at a distance equal to the radius of the circle.

    Is this valid to do? I am sure there would be an easier way to solve this problem, but just out of curiosity, would this work?
     
  2. jcsd
  3. Dec 23, 2013 #2

    CAF123

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    I don't think it would be valid. In the case of a circular source of charge with the centre of the circle at point P, all the charge elements are at a distance r away. If instead you keep P fixed, but put a horizontal line of charge a distance r away, not all the charge elements (or points on that line) will be at a distance r from P.
     

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  4. Dec 23, 2013 #3
    Ok, that makes sense. What about if it was a ring with constant current through it and you were looking for the b field at the center. Would it work in this case?
     
  5. Dec 23, 2013 #4

    CAF123

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    No, for the same reason, the current elements are not all the same distance from the point of interest. Using the Biot-Savart law, you can derive explicit expressions for the B field at the centre of the loop from a circular current flow and that from a wire.
     
  6. Dec 23, 2013 #5
    Just apply Gauss's law and you're ready to go.

    The scenario you described corresponds to a closed surface. Therefore, you need the area of the circle, not it's perimeter.
     
  7. Dec 23, 2013 #6
    Shouldn't the electric field at the center of the circle be zero as a result of the symmetry of the geometry. Which direction would you think the electric field vector at the center of the circle would be pointing?

    Chet
     
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