Question

7. Four equal charges, each of + 7.0 /C are placed at the corners of a 0.50 m x 0.75 m rectangle (a) Calculate the direction and magnitude of the electric force F., on gı due to the other three charges. (b) Find the direction and magnitude of the electric field E at point P. (See Figure 1.) 42 0.75 m 93 0.50 m qi q4 Figure 1

Answer 1

Force on q_1 due to q-4, F_4 = k times 7 times 7 times 10^- 12/(0.75)^2 similarly F_2 = k times 49 times 10^- 12/(.5)^2 = 1.764 N F_3 = k times 48 times 10^- 12/(.5^2 + .75^2) = .543 F_3 has two components, F_3 cos theta, F_3 sin theta cos theta = -75/squareroot .5^2 + .75^2 = 0.083 sin theta = .5/.901 = .554 Total force in x-dir^n = F_3 sin theta + F_4 = .543 times .554 + .784 = 1.08 N Total forces in-y dir^n = F_2 + F_3 cos theta = 1.76 + .543 times .83 = 2.21 N So resultant Forces = squareroot (2.21)^2 + (1.08)^2 = 2.459N tan theta = 1.08/2.21 = nu = 26 degree clockwise from -y axis Electric Field will be zero, an E_1 cancels out E_3 & E_2 cancels out E_4