1. A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies? a. 81 N/C b. 61 N/C C. 71 N/C d. 51 N/C e. 25 N/C 2. A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC. What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod? a. 40 N/C b. 45 N/C C . 24 N/C d. 90 N/C e. 36 N/C 3. A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis? 36dx a. b. 4 154dx 4 36dx Jo (10-x) 2 Jo (10-x) 2 C. Jo x2 d. 10 154dx e. none of these x2 4. A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis? 21 6dy 54dy a. Jo ( 4+2) 312 b. (4 10ady Jo ( 4 + 1 2 ) 312 C. Jo 4ty ? 27dy d. Jo 4+yz e . none of these 5. A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m. Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis? 27dy b. 27dy 135dy a. J 3 ( 4 -y) 2 J -3 76 + 12 C. J 3 74 - 1)2 d. 135dy -3 16+2 e . none of these 6. A uniformly charged rod (length = 2.0 m, charge per unit length = 5.0 nC/m) is bent to form one quadrant of a circle. What is the magnitude of the electric field at the center of the circle? a. 62 N/C b. 56 N/C C. 50 N/C 44 N/C e. 25 N/C.7. A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +8 m on the x axis? a. 6 54dx b. (6 21 6dx 6 54dx J2 ( 8 - x) 2 12 (8 - x ) 2 C . J2 x2 d. 6 21 6dx J2 e. none of these x2 8. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis? -18xdx -18dx a. J ( 4 + x2 ) 3/2 b. 0 ( 2 + x ) 2 C. -18dx 4+ x 2 d. ['s -18xdx ( 2 + x ) 3 e . none of these 9. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis? 72dx b. 18dx a. Jo 3 72dx ( 16 + x 2 ) 31 2 0 (16+ x2 ) 31 2 C. Jo 16+x 2 d. Co 18dx J3 16+ x 2 e. none of these 10. A uniformly charged rod (length = 2.0 m, charge per unit length = 3.0 nC/m) is bent to form a semicircle. What is the magnitude of the electric field at the center of the circle? a. 64 N/C b. 133 N/C C. 48 N/C d. 85 N/C e. 34 N/C 11. A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m. a. 81 N/C b. 74 N/C C. 61 N/C d. 88 N/C e. 20 N/C 12. Two uniform rods, each of length 2.0 m, are bent to form semicircles. One rod has a charger per unit lent of 1.5 nC/m, and the other has a charge per unit length of -1.5 nC/m. The semicircles are joined to make a circle. What is the magnitude of the electric field at the center of the circle? 42 N/C b. 84 N/C C. 34 N/C 68 N/C e. 0