1 answer

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

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. Well 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

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

Answers

a) Central charge is at a distance of L from each of the other charges Force on central charge Qdue to charges-5 opposite, so they cancel each other at top left corner, and-5Q at bottom right comer are equal and Force on central charge Qdue to charges-5Q at bottom left comer, and-5at top right cormer are equal and opposite, so they cancel each other Force on central chargedue to charges +2 they cancel each other at top middle and +2Q at bottom middle are equal and opposite, so Force on central charge due to charges+3 direction, that is along positive X-axis at left middle and-3Q at right middle are equal and act in the same Net force on central chargeQ due to +3 and-3Qis kQ* 3Q rQ = 2T2_ = 2 * 8.99 * 10.3 * (6 * 10-6)2 (0.60)25.39 V b) Magnitude of force on-3 by +2Q at Magnitude of force on-3 by-5Q at top left charge is The magnitude of force exerted on-3Qcharge by the +2 charge at the top is equal to the magnitude of top middle charge is rre force exerted on-3Q charge by the-5Qcharge at top left. The -3 charge exerts a force on +2Q charge that has the same magnitude as the force +2Q charge exerts on charge c) Force exerted on-3Q due to +3 and+Qis along towards negative X.axis (21)2 F-8.99096102 (2 0.60)2 +8.99 10 3(6+ 10-92 0.602 F-30.1 4.72 N d) Force exerted on -3 cancel each other. due to charge-5Q at top right and-5Q at bottom right are equal and opposite, so they The vertical components force exerted on -3Q due to charge -5Qat top left and -5 at bottom left will cancel each other, the horizontal components of force exerted on-30 due to charge5at top left and-5 at bottom left will add up to give force in the direction of positive X-axis2L 5 where cos COSけ r_IQ.2=2*8.99 * 109 * 15 * (6*10-6)2 2 (V5 0.60)2 V5 3Q.2 4.82 N e) The vertical components force exerted on-3Q due to charge +2Q at top middle and+2 cancel each other, the horizontal components of force exerted on at bottom middle will add up to give force in the direction of negative X-axis at bottom middle will at top middle and +2Q -3Q due to charge +2 k3Q * 2Q V2 where cos θ r_3Q.3 = 2 * 8.99 * ]0. 6 * (6 * 10-6)2 (V2 * 0.60)2 V2 F-303 3.81 N Net force on the charge-3Qis r_3Q =-4.72 4.82 _ 3.81 =-3.71 M Magnitude of force experienced by charge-3Q due to 8 charges is! F-39-371 N g) Direction force is towards negative X-axis left

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