Three point charges are located on the x-axis. The first charge, q₁ = 10.0 µC, is at x = −1.00 m; the second charge, q₂ = 20.0 µC, is at the origin; and the third charge, q₃ = −30.0 µC, is located at x = 2.00 m. What is the force on q₂? A) 1.65 N in the negative x-direction B) 3.15 N in the positive x-direction C) 1.50 N in the negative x-direction D) 4.80 N in the positive x-direction E) 4.65 N in the negative x-direction

Question

Quizplus · Accepted Answer

The force on q2 is due to the charges q1 and q3. The force due to q1 is in the negative x-direction, and the force due to q3 is in the positive x-direction. The net force on q2 is the vector sum of these two forces, which is in the positive x-direction. The magnitude of the net force is:$$F = k\frac{|q_1q_2|}{r_{12}^2} + k\frac{|q_2q_3|}{r_{23}^2}$$$$= (9	imes10^9\frac{	ext{Nm}^2}{	ext{C}^2})\frac{(10	imes10^{-6}	ext{C})(20	imes10^{-6}	ext{C})}{(1	ext{m})^2} + (9	imes10^9\frac{	ext{Nm}^2}{	ext{C}^2})\frac{(20	imes10^{-6}	ext{C})(-30	imes10^{-6}	ext{C})}{(2	ext{m})^2}$$$$= 3.15	ext{ N}$$Therefore, the force on q2 is 3.15 N in the positive x-direction.

Three Point Charges Are Located on the X-Axis