Question

In the figure below, each charged particle is located at one of the four vertices of a square with side length a. In the figure, A-3, B-4, and C= 8, and q > 0. (a) What is the expression for the magnitude of the electric field in the upper right corner of the square (at the location of q)? (Use the following as necessary: q, a, and ke) Give the direction angle (in degrees counterclockwise from the +x-axis) of the electric field at this location. ° (counterclockwise from the +x-axis) (b) Determine the expression for the total electric force exerted on the charge q. (Enter the magnitude. Use the following as necessary: q, a, and ke.) Give the direction angle (in degrees counterclockwise from the +x-axis) of the electric force on q (counterclockwise from the +x-axis) (c) What If? How would the answers to parts (a) and (b) change if each of the four charges were negative with the same magnitude? Select all that apply. The electric field would be the same magnitude and direction as the field in part (a) The force would be the same magnitude and direction as the force in part (b) The force would be the same magnitude but opposite direction as the force in part (b). The electric field would be the same magnitude but opposite direction as the field in part (a)

Answer 1

a) E_x = k.3q/a^2 + 1/squareroot 2 k.4q/(squareroot 2 a)^2 = (3 + squareroot 2) k q/a^2 = 4.414 kq/a^2 E_y = 5.8q/a^2 + 1/squareroot 2 k.4q/(squareroot 2 a)^2 = (8 + squareroot 2) k q/a^2 = 9.414 kq/a^2 E = squareroot E_x^2 + E_y^2 = 10.397 kq/a^2 Direction, theta = tan^- 1 (E_y/E_x) = 64.88 degree b) F = qE = 10.397 kq^2/a^2 theta = 64.88 degree c) Force would have the same magnitude and direction as part 'b' Electric field would be same magnitude but opposite direction as part 'b'