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solve all parts Three point charges are arranged in a horizontal line as shown b

ID: 1526977 • Letter: S

Question

solve all parts

Three point charges are arranged in a horizontal line as shown below. Find the electric forces (in units of kQ^2/R^2) on the charges given the following: Q_1 = -80 Q, Q_2 = -4 Q, Q_3 = 36 Q, r_1 = 4 R and r_2 = 2 R Remember that a positive force points to the right and a negative force points to the left. What is the net force on charge Q_1? What is the net force on charge Q_2? The total force on Q_2 is going to be a vector sum of F_2: (the force on Q_2 due to Q_1) and F_23 (the force on Q_2 due to Q_3). You need to find both the magnitudes and directions of F_21 and F_23. The magnitudes of the forces are given by: F_21 = kQ_2Q_1/r_1^2 and F_23 = kQ_2Q_3/r_2^2, where k = 9e9 Vm/C and the absolute values for all charges should be used. The direction of each force is determined by the two charges, where opposite charges attract and same charges repel. What is the net force on charge Q_3? What is the sum of the forces on all three charges?

Explanation / Answer

On charge Q1 :

F3 = force by charge Q3 = k Q1 Q3/r12 = k (80 Q) (36Q)/(4R)2 = 180 kQ/R2    towards right

F2 = force by charge Q2 = k Q1 Q2/(r1 + r2 )2 = k (80 Q) (4Q)/(6R)2 = 8.88 kQ/R2     towards left

Net force on Q1 = F3 - F2 = 180 kQ/R2 - 8.88 kQ/R2 = 171.12 kQ/R2

On charge Q2 :

F3 = force by charge Q3 = k Q2 Q3/r22 = k (4 Q) (36Q)/(2R)2 = 36 kQ/R2    towards left

F1 = force by charge Q1 = k Q1 Q2/(r1 + r2 )2 = k (80 Q) (4Q)/(6R)2 = 8.88 kQ/R2     towards left

Net force on Q1 = F3 + F1 = 36 kQ/R2 + 8.88 kQ/R2 = 44.88 kQ/R2    towards left

On charge Q3 :

F2 = force by charge Q2 = k Q2 Q3/r22 = k (4 Q) (36Q)/(2R)2 = 36 kQ/R2    towards right

F1 = force by charge Q1 = k Q1 Q3/(r1 )2 = k (80 Q) (36Q)/(4R)2 = 180 kQ/R2     towards left

Net force on Q3 = F1 - F2 = 180 kQ/R2 - 36 kQ/R2 = 144 kQ/R2    towards left