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A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge -Q is distributed uniformly around the right half of the semicircle (Fig. P21.86). What are the magnitude and direction of the net electric field at the origin produced by this distribution of charge?

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The electric field that is at the center of a charged circular quadrant identical to that of a charged circular arc. It’s calculated by taking into account a tiny elemental charge in the arc, which creates an angle at the point of origin that is only one set of arc. As we are aware of the electric field caused by an elemental point charge at a distance, what is carried out here. We calculate the electric field caused by the point charge that is small in size at the point of origin. Then, after adding with the equation of electric fields, taking limits of 0 to the angle created by the arc at its point of origin, we can find the equation of the field electric that is at the source caused by the charged arc:

E = (2kλsinθ) ⁄ R

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