Nine different charged balls, which we treat as point charges, are arranged in a

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 5.00 times 10^-6 C, and L = 50.0 cm What is the magnitude of the net force experienced by the ball with the +Q 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. 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 -30 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 -SQ at the top left of the square. The -30 charge exerts a larger magnitude force on the +20 charge than the +20 charge exerts on the-3Q charge. The -3Q charge exerts a smaller magnitude force on the +2Q charge than the +20 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 300 charge by the +20 charge at the top is larger than the magnitude of the force exerted on the 39 charge by the 50 charge at the top left. The magnitude of the force exerted on the -3Q charge by the +2Q 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. What is the magnitude of the net force experienced by the ball with the -30 charge due to the +3Q and +9 charged balls only? What is the magnitude of the net force experienced by the ball with the 30 charge due to the four charged balls with charges of -50? 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.

Explanation / Answer

b)
1) False

2) False

3) True

4) False

5) True

6) False

c) 4.75 N (towards -x axis)

d) force between -3*Q and 5*Q, F35 = 9*10^9*15*(5*10^-6)^2/(5*0.5^2)

= 2.7

force due to 4 -5*Q charge = 2*F35*cos(theta)

= 2*2.7*2/sqrt(5)

= 4.83 N (towards -x axis)

e) force between -3*Q and 2*Q, F25 = 9*10^9*6*(5*10^-6)^2/(0.5^2)

= 5.4

force due to two +2*Q charge = F25*sqrt(2)

= 5.4*sqrt(2)

= 7.64 N (towards -x axis)

f) net force = 4.75 + 4.83 - 7.64

= 1.94 N

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