Question

10 Figure 22-38a shows two charged particles fixed in place on an x axis with separation L. The ratio qilą2 of their charge mag- nitudes is 4.00. Figure 22-38b shows the x component Enet.x of their net electric field along the x axis just to the right of particle 2.The x axis scale is set by x, 30.0 cm. (a) At what value of x > 0 is Enet.x maximum? (b) If particle 2 has charge --3e, what is the value of that maximum? +q1 -42 0 ︶-2 -4 x (cm) Figure 22-38 Problem 10.

Answer 1

E_net, x = q_1/4 pi elementof_0 1/(X + L)^2 - q_2/4 pi elementof_0 (X^2) Maximum field when d E_net, y/d x = 0 d E_net, y/d x = 0 1/4 pi elementof_0 [- q_1 2/(X + L)^3 + 2 q_2/X^3] = 0 \r\n q_1/(X + L)^3 = q_2/X^3 q_1/q_2 = (X + L/X)^3 x + l/lambda = (q_1/q_2)^1/3 X + L = x (q_1/q_2)^1/3 x((q_1/q_2)^1/3 - 1) = L X = L/[q_1/q_2)^1/2 - 1] X = 1070 L \r\n field at X = 1.70 L E_net = q_1/4 pi elementof_0 (X + L)^2 - q_2/4 pi elementof_0 (X)^2 q_1/q_2 = 4 (q_2) = 3 e q_1 = 12 e E_net = 12 e/4 pi elementof_0 (2.7 L)^2 - 3e/4 pi elementof_0 (1.7 L)^2 = 9 times 10^9 e/L^2 [12/(2.7)^2 - 3/(1.7)^2] = 9 times 10^9 times 1.6 times 10^-19/12 times (0.61) E_net = 8.74 times 10^-10/L^2 \r\n field is zero at X_s = 60 cm E_field = q_1/4 pi elementof_0 (X + L)^2 - q_2/(X^2) (4 pi elementof_0) q_1/(X + L)^2 = q_2/X^2