Help finding the Electric field at the center of charged arc

In summary, the length of the charged area is pi*R/2 and this is because the total circumference of a circle is 2*pi*R and we are only evaluating a quarter of the circle, so we divide by 4 to get pi*R/2. This is then multiplied by the charge +Q to get 2Q/pi*R. Your teacher's solution is a good approach to solving this problem.
  • #1
guyvsdcsniper
264
37
Homework Statement
Determine electric field at center of curvature of arc.
Relevant Equations
E=KQ/r^2
I am having trouble understand where area circled in red.

I get that lamda is Q/L. The charge is +Q. Length is pi/R/2.

I am having trouble understanding why the length is pi/R/2? Is it because the circumference of a circle is 2*pi*R and since we have broken this problem down to just evaluating a quarter of the a circle, we divide 2*pi*R by 4 and get pi*R/2 which when we put that under Q we get 2Q/pi*R?

I wasnt sure until I typed out my question about and believe that may be the case, but just looking for some conformation.

Also, is there a simpler approach to this problem? My teacher wrote this out and I found it hard to follow.
 

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  • #2
quittingthecult said:
I am having trouble understanding why the length is pi/R/2? Is it because the circumference of a circle is 2*pi*R and since we have broken this problem down to just evaluating a quarter of the a circle, we divide 2*pi*R by 4 and get pi*R/2 which when we put that under Q we get 2Q/pi*R?

I wasnt sure until I typed out my question about and believe that may be the case, but just looking for some conformation.
Yes, I think you have correctly answered your own question. The charge +Q is spread out over a length of a quarter of a circle of radius R.
quittingthecult said:
Also, is there a simpler approach to this problem? My teacher wrote this out and I found it hard to follow.
Your teacher's solution looks very good. If there is a specific place in the solution that you are confused about, we can help clarify.
 

1. What is the formula for calculating the electric field at the center of a charged arc?

The formula for calculating the electric field at the center of a charged arc is E = kQ/r, where E is the electric field, k is the Coulomb's constant, Q is the charge of the arc, and r is the distance from the center of the arc to the point where the electric field is being calculated.

2. How do I determine the direction of the electric field at the center of a charged arc?

The direction of the electric field at the center of a charged arc is determined by the direction of the electric field vectors of each individual charge in the arc. If the charges in the arc are all positive, the electric field will point away from the center of the arc. If the charges are all negative, the electric field will point towards the center of the arc.

3. Can the electric field at the center of a charged arc be zero?

Yes, the electric field at the center of a charged arc can be zero if the arc is made up of an equal number of positive and negative charges, and they are distributed symmetrically around the center. This will result in the electric field vectors cancelling each other out, resulting in a net electric field of zero at the center.

4. How does the distance from the center of the arc affect the electric field?

The electric field at the center of a charged arc is inversely proportional to the distance from the center of the arc. This means that as the distance increases, the electric field decreases. This relationship is described by the formula E = kQ/r, where r is the distance from the center of the arc.

5. Can the electric field at the center of a charged arc be negative?

Yes, the electric field at the center of a charged arc can be negative if the charges in the arc are not distributed symmetrically around the center. This will result in a net electric field that points in the opposite direction of the majority of the individual electric field vectors, resulting in a negative value.

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