Question

Nine different charged balls, which we treat as point charges, are arranged in a highly symmetric pattern around a square. Note that the value of Q is 6.00 x 10-6 C, and L = 60.0 cm. 2050 2L 50 50 2L (a) What is the magnitude of the net force experienced by the ball with the + charge at the center of the square, due to the other 8 charged balls? For the rest of this problem, we will consider the forces acting on the ball of charge -3Q. (b) Select the two correct statements from the six statements below. Note that you must select both correct statements, and no incorrect statements, to get credit for the question. We'll consider first the force exerted on the ball of charge -3Q by the ball of charge +2Q at the top of the square, and then compare it to the force exerted on the ball of charge -3Q by the ball of charge -5Q at the top left of the square. The -3Q charge exerts a larger magnitude force on the +2Q charge than the +2Q charge exerts on the -3Q charge. The -3Q charge exerts a smaller magnitude force on the +2Q charge than the +2Q charge exerts on the -3Q charge. The -3Q charge exerts a force on the +2Q charge that has the same magnitude as the force the +2Q charge exerts on the -3Q charge. The magnitude of the force exerted on the -3Q charge by the +2Q charge at the top is larger than the magnitude of the force exerted on the -3Q charge by the -5Q charge at the top left. The magnitude of the force exerted on the -3Q charge by the +2 charge at the top is smaller than the magnitude of the force exerted on the -3Q charge by the -5Q charge at the top left. The magnitude of the force exerted on the -3Q charge by the +2Q charge at the top is equal to the magnitude of the force exerted on the -3Q charge by the -5Q charge at the top left. (c) What is the magnitude of the net force experienced by the ball with the-3Q charge due to the +3Q and +Q charged balls only? (d) What is the magnitude of the net force experienced by the ball with the-3Q charge due to the four charged balls with charges of 5Q? (e) What is the magnitude of the net force experienced by the ball with the -3Q charge due to the two charged balls with charges of +2Q? () Use your previous three results to find the magnitude of the net force experienced by the ball with the -3Q charge due to the other 8 charged balls (g) In what direction is the net force experienced by the ball with the -3Q charge due to the other 8 charged balls? (Select all that apply. For instance, if the net force has a component directed down and a component directed left, you would select both down and left.) Up down left O right

Answer 1

a) Central charge q is at a distance of L from each of the other charges. Force on central charge Q due to charges -5Q at top left corner, and -5Q at bottom right corner are equal and opposite, so they cancel each other. Force on central charge Q due to charges -5Q at bottom left corner, and -5Q at top right corner are equal and opposite, so they cancel each other. Force on central charge Q due to charges + 2Q at top middle and + 2Q at bottom middle are equal and opposite, so they cancel each other. Force on central charge Q due to charges + 3Q at left middle and -3Q at right middle are equal and direction, that is along positive X-axis. Net force on central charge Q due to + 3Q and -3Q is F_Q = 2 kQ * 3Q/L^2 = 2 * 8.99 * 10^9 * 3 * (6 * 10^-6)^2/(0.60)^2 = 5.39 N