Question

66. l Three 1.0 nC charges are -10nc placed as shown in FIGURE P22.66. Each of these charges creates an electric field E ata point 3.0 cm in front of the middle charge a. What are the three fields 1.0 cm IOnC -30cm.. 1.0 cm FIGURE P22.66 El, E2, and E, created by the three charges? Write your answer for each as a vector in component form. b. Do you think that electric fields obey a principle of super position? That is, is there a "net field" at this point given by Ene.-E, + E2 + E3? Use what you learned in this chapter and previously in our study of forces to argue why this is or is not true. c. If it is true, what is Enct?

Answer 1

The solution is given in the attached image.

Final answers are boxed. The explanation is provided.

Q_1 = 1 nC, q_2 = 1 nC, q_3 = 1 nC (a) E_1^vector = 1/4 pi q_0 q_1/r_1^2 r_1^ r_1^= 3i^- j^/squareroot 10 implies E_1^vector = 9 times 10^9 times 10^-9/10 times (3i^- j^/squareroot 10) = 2.7 i^/squareroot 10 - 0.9 j^/squareroot 10 N/C E_2^vector = 1/4 pi q_0 q_2/r_2^2 r_2^, r_2^= 3 i^/3 E_2^= 9 times 10^9 times 10^-9/9 times (3 i^/3) = i^. N/C E_3^vector = 1/4 pi q_0 q_3/r_3^2 r_3^, r_3^= 3i^+ j^/squareroot 10 = 9 times 10^9 times 10^-9/10 times (3 i^+ j^/squareroot 10) = 2.7 i^/squareroot 10 + 0.9 j^/squareroot 10 N/C (b) since, Electric fields, E_1^vector, E_2^vector and E_3^vector are vectors of same dimensions and vectors always superpose at every point given they are of same dimensions. Hence, they will so follow principle of superposition. (c) E_net^vector = E_1^vector + E_2^vector + E_3^vector = 2.7 i^/squareroot 10 - 0.9 i^/squareroot 10 + i^+ 2.7 i^/squareroot