Three point charges are located at the vertices of an equilateral triangle of side length l = 10 cm. We know that (:11 = 2 uC, q2 = 3 \"C, and (:13 is negative, but we do not know the magnitude of (:13. (a) If the magnitude of the net electric force on (:13 is 31.4 N, what is the value of q3? (b) What is the total electric field at the center of the triangle? If you were not able to solve for q3 in part (a), use (13 = 1 [AC (This is not the correct value, so do not be concerned if the value you found in part (a) is different). 2. Two point charges are placed on the x-axis. One charge q1 = 5 pC is placed at x = 0, and the second charge q2 = 7 pC is placed at x = 100 cm. A third point charge q3 is placed somewhere on the x-axis, and it experiences zero net force. What is the location of qg? 3. A line charge sits on the y-axis between 31 = 0 and y = L. The line charge has a total charge of Q, where Q > 0. P Find the electric field produced by the line charge at some point P on the x-axis. Hint: you may find the following integral useful = 4 + constant 1 l (x2 + yam xZJxz + y2 4. Positive charge Q is distributed uniformly around a semicircular arc of radius R. y x Find the electric field produced by the arc at the origin of the coordinate system. 5. Charge is distributed nonuniformly around a semicircular arc of radius R. The linear charge density of the arc is 11(6) = 10 cos 6, where 210 is a positive constant. y M9) = 10 cos 9 (a) Calculate the net charge ofthe distribution. (b) Find the electric field produced by the arc at the origin of the coordinate system. The cube shown below is immersed in a nonuniform electric field E" = axi + bj', where a and b are constants. z 53 (top) 31 (left / S6 (back) side)\\ ' / 8;; (right side) V 55 (front) S4 (bottom) (a) Calculate the electric flux through each face of the cube for a = 3 x 105 % , b = 4x 103 %,andL = 10cm. (b) What is the net charge enclosed by the cube