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

1. Dec 23, 2013

### Yosty22

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. Dec 23, 2013

### CAF123

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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3. Dec 23, 2013

### Yosty22

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?

4. Dec 23, 2013

### CAF123

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.

5. Dec 23, 2013

### CaptainHammer

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.

6. Dec 23, 2013

### Staff: Mentor

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