Question

Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 µC at x = 0, +20 µC at x = 40 cm, and –60 µC at x = 60 cm, what is the magnitude of the electrostatic force on the +32-µC charge? *

Answer 1

Magnitude of the electrostatic force on the +32 µC charge,
`F_(net) = 12 N`

Step-by-step explanation:

Let q₁ = +32 µC, x₁ = 0

q₂ = +20 µC, x₂ = 40 cm = 0.4 m

q₃ = -60 µC, x₃ = 60 cm = 0.6 m

Let magnitude of the electrostatic force on the +32 µC charge due to the + 20 µC charge = F₁ (i.e force on q₁ due to q₂)

`F_(2) = (kq_(1)q_(2) )/(x_(2)^2 )`

`F_(2) = (9 * 10^(9) * 32 * 10^(-6) * 20 * 10^(-6) )/(0.4^2 )\\F_(2) = 36 N`

Let magnitude of the electrostatic force on the +32 µC charge due to the -60 µC charge = F₂ (i.e force on q₁ due to q₃)

`F_(3) = (kq_(1)q_(3) )/(x_(3)^2 )`

`F_(3) = -(9 * 10^(9) * 32 * 10^(-6) * 60 * 10^(-6) )/(0.6^2 )\\F_(3) =-48 N`

The electrostatic force on the 32 µC charge,
`F_(net) = |F_(2) + F_(3)|`

`F_(net) =| 36 + (-48)| \\F_(net) =|- 12 N| \\ F_(net) = 12 N`