with detailed solution used the formula given

21.84 .. CALC A semicircle of Figure P21.84 radius a is in the first and second quadrants, with the center of cur- vature at the origin. Positive charge + Q is distributed uniformly around + Q Q the left half of the semicircle, and negative charge -Q is distributed uniformly around the right half of the semicircle (Fig. P21.84). What are the magnitude and direction of the net electric field at the origin produced by this distribution of charge?21.27 .. CP An electron is pro- Figure E21.27 jected with an initial speed vo = K-2.00 cm 1.60 X 10 m/s into the uniform field between two parallel plates (Fig. E21.27). VO Assume that the field between the plates 1.00 cm E is uniform and directed vertically down- ward and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. (a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. (b) Suppose that the electron in Fig. E21.27 is replaced by a proton with the same initial speed vo. Would the proton hit one of the plates? If not, what would be the magnitude and direction of its vertical displacement as it exits the region between the plates? (c) Compare the paths traveled by the elec- tron and the proton, and explain the differences. (d) Discuss whether it is reasonable to ignore the effects of gravity for each particle.In this chapter we learned about Coulomb's Law - 1 . 1 9 .N 2 I'II'IZI where k _ = 8399 x l] m F = k _ T2 471350 6'2 we also found out that the electric eld is F E : 0 were 90 is the test charge and F0 is the force on the test charge. 9'0 This then gives us tr: . E : Twhere qu the source charge. 1* we then solved for the electric elds of a straight line, a ring of charge, a charged disk, and infinite sheet and two parallel plates. Finally, we learned about electric dipoles where the Torque is given by T = p X E where p is the dipole Inc-meat. p = qd. and the potential energy is given by U'=p-E 21.38 .. A point charge is placed at Figure E21.38 each corner of a square with side length + 9 + 9 a. All charges have magnitude q. Two of the charges are positive and two are nega- tive (Fig. E21.38). What is the direction of the net electric field at the center of the a square due to the four charges, and what is its magnitude in terms of q and a