Electric field at the center of a Charged Circular Arc

Note : when the lines are red - the applet is calculating the electric field .. wait a second for it to finish.

[Also, this is not a "perfect" simulation - using point charges instead of a uniform "charge/unit length" arc gives us the right conceptual picture, but this is meant only for the concepts, not the exact calculations.]

Introduction : This applet illustrates the Electric field at the center of a circle, assuming that part of the circle is charged (a charged "arc" of the circle). We simulate the charged arc with a collection of point charges around the arc. We can increase the angle of the charged arc (really the "half angle" from the horizontal axis to above and below the axis (with 90 degrees creating a half circle).

Note : The simulation starts with just one charge - and the initial electric field at the center is just the Electric field of a point charge.

Set the arc "half angle" :
      Angle (degrees) =    

We can see what the electric field at the center is (keep in mind that this value is really E/k) :

Questions :
a) What happens as we increase the angle, the field at the center increases, right ... what about if the angle is greater than 90 degrees, the E field goes down? Why?
b) Notice the first charge creates an E field of 0.1 (=0.225/(1.5)2) .. and the first three create a field of 0.3 .. but the first 5 create a field of only 0.48 (less than the 0.5 expected) - why is this?

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