Three point charges are located at the following positions: Q1 = 2.00 microC at

Question

Three point charges are located at the following positions: Q1 = 2.00 microC at x = 1.00 m; Q2 = 3.00 microC at x = 0; Q3 = -5.00 microC at x = -1.00 m. What is the magnitude of the force on the 3.00-microC charge?

Two point charges, separated by 1.5 cm, have charge values of 2.0 and -4.0 microC, respectively. What is the magnitude of the electric force between them?

Two point charges of +3.0 microC and -7.0 microC are placed at x = 0 and x = 0.20 m. What is the magnitude of the electric field at the point midway between them?

Explanation / Answer

1)The point charges and their positions are:
Q1 = 2.00 microC at x = 1.00 m; Q2 = 3.00 microC at x = 0; Q3 = -5.00 microC at x = -1.00 m. The force between the charges Q1 and Q2 is F1 = k * (Q1 * Q2/r^2) where k = (1/4peo) = 9 * 10^9 Nm^2/C^2,Q1 = 2.00 µC = 2.00 * 10^-6 C,Q2 = 3.00 µC = 3.00 * 10^-6 C and r = (1.00 - 0) m = 1.00 m The force between the charges Q2 and Q3 is F2 = k * (Q2 * Q3/r1^2) where Q3 = -5.00 µC = -5.00 * 10^-6 C and r1 = (0 - (-1.00) m = 1.00 m The magnitude of the force on the 3.00-microC charge is Fnet = F1 + F2 = k * (Q1 * Q2/r^2) + k * (Q2 * Q3/r1^2) = k * Q2 * (Q1/r^2 + Q3/r1^2) 2)The distance between the charges is r = 1.5 cm = 1.5 * 10^-2 m The charges are Q1 = 2.0 µC = 2.0 * 10^-6 C and Q2 = -4.0 µC = -4.0 * 10^-6 C The magnitude of the electric force between them is F = k * (Q1 * Q2/r^2) 3)The two point charges are Q1 = +3.0 µC = +3.0 * 10^-6 C and Q2 = -7.0 µC = -7.0 * 10^-6 C.The position of the charges is at x = 0 and x = 0.20 m The electric field due to the charge Q1 is E1 = k * (Q1/r1^2) where r1 = 0.10 m The electric field due to the charge Q2 is E2 = k * (Q2/r2^2) where r2 = 0.10 m The magnitude of the electric field at the point midway between them is Enet = E1 + E2 = k * (Q1/r1^2) + k * (Q2/r2^2) = k * ((Q1/r1^2) + (Q2/r2^2))

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