Question

Three positive point charges are located at the corners of a rectangle, as illustrated in the figure below. Find the electric field (in N/C) at the fourth corner if q1 = 9 nC, q2 = 8 nC, and q3 = 7 nC. The distances are d1 = 0.6 m and d2 = 0.2 m. (Let the positive x-direction be to the right, and the positive y-direction be upward.)

Answer 1

use the electric field concept to calculate net field.

Use the electric field concept to calculate net field. The x component field concept to calculate net filed is, E_x = E_2 - E_3 cos 45 = -[k q_2/d_1^2 + k q_3/d_1^2 + d_2^2 cos 45] = -[(9 times 10^9) (8 times 10^-9)/(0.6)^2 + (9 times 10^9) (7 times 10^-9)/0.6^2 + 0.2^2 cos 45] = -(200 + 11.369) = -311.37 N/C The y component of electric field is, E_y = E_1 + E_3 sin 45 = [k q_1/d_2 + k q_3/d_1^2 + d_2^2 sin 45] = [(9 times 10^9) (9 times 10^-9)/(0.2) + (9 times 10^9) (7 times 10^-9)/0.6^2 + 0.2^2 sin 45] = (405 + 111.369) = 516.37 N/C The net field is, E = squareroot E_x + E_y = squareroot -311.37 + 516.37 = 205 N/C