S' Semi Circular are, y-axis. radius R do x-axis Figure 4: A uniformly charged semi-circular arc of radius R. A is the charge per unit length. 5. Field of a semi-circular arc A semi-circular arc of radius R has a charge per unit length . We wish to compute the electric field E at P, the center of the arc. (a) What is the total charge of the a c? (b) In what direction does E point? Explain briefly. (c) Consider the infinitesimal segment of arc located at an angle 0 from the x-axis. de is the angle subtended by this segment at as shown in figure 4. (i) What is the charge of this segmert? (ii) What is the distance of this segn ent from P? (iii) Write down the displacement vector R from the segment to P. Give your answer in terms of R, 0, i and . (iv) Using Coulomb's law write down the electric field dE at P that is produced by the infinitesimal arc segment. (d) By integration of the result of part (c) determine Ex, the x-component of the total electric