Question

Four charges, Aq, Bq, Cq, and Dq (where q-2.00 ×10-, C), sit in a plane at the corners of a square whose sides have length d = 37.5 cm, as shown in the diagram below. A charge, Eq, is placed at the origin at the center of the square. (Note that A, B, C, D, and E are integer multipliers.) Ag Bq Eq Dq Cq square of side length, d DATA: A-6, B 2, C 7, D-8, E = 2. Consider the charge at the center of the square, Eq. what is the net x-component of the force on this charge? 4pts Submit Answer Tries 0/10 What is the net force, in the y-direction, on the center charge, Eq? 4pts Submit Answer Tries 0/10 Consider the situation where A=B=C=D=1, E=-1, and the following statements. Select "True" or "False" for each statement. FalseIf one were to double the magnitude of the upper-right-hand positive charge, the negative charge would be in equilibrium. FalseThe sum of the forces on the center charge in the x-direction equals zero FalseThe sum of the forces on the center charge in the y-direction equals zero True If one were to triple the magnitude of the negative charge, the negative charge would not be in equilibrium False The equilibrium point at the center is an unstable equilibrium for the motion of the negative charge in the line from the center charge and perpendicular to the plane of the square

Answer 1

Distance from centroid to each corner of square is r = squareroot (d/2)^2 + (d/2)^2 = d/squareroot 2 = 37.5 times 10^-2 m/squareroot 2 r = 0.265 m X - Component of electric field at E_epsilon due to corners A, B, C, D is F_x = -kA_q E_q/(r)^2 cos(45 degree) + kB_q E_q/(r)^2 cos(45 degree) + kC_q E_q/(r)^2 cos(45 degree) + kd_q E_q/(r)^2 cos (45 degree) = [-A_q + B_q + C_q - D_q] kE_q^2/r^2 cos 45 = [-6 + 2 + 7 - 8] 9 times 10^9 times 2 times (2 times 10^-7)^2/(0.265)^2 cos 45 degree = -0.0362 \r\n Y - Component of electric field at E_q due to corners A, B, C, D is F_y = kA_q E_q/(r)^2 sin 45 degree + kB_r E_q/(r)^2 sin 45 degree - kC_q E_q/r^2 sin 45 degree - kD_q E_q/r^2 cos 45 = [A_q + B_q - C_q - D_q] kE_q^2/r^2 cos 45 degree = [6 + 2 + 7 - 8] times 9 times 10^9 times 2 times (2 times