### Find the magnitude of the electric field at the center

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A charged line of linear charge density ? has been bent into a circular arc of radius r that makes an angle ? with its center. (A). Find the magnitude of the electric field at the center of this arc. (Does your result make sense, what should it be if the arc were increased to a full circle? How about if it were shrunk to an angle of 0?) (B). Where would a point charge of the same total charge as the arc need to be placed in order to make the electric field at the center of the arc equal to zero? (Hint: X and Y axes have not been chosen for you, you will have to choose your own. If you consider symmetry, you can choose them so that the electric field at the center only points in either the X or Y direction. Make sure to include a diagram showing your choice. More Hints: How does the magnitude of the electric field contributed by each little segment of arc compare to the contributions from the other segments? Do we just straight up add these magnitudes?)

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