Question

Two electric point charges are moved from really far away to points on the positive x axis. Q1 is placed at x = b. Q2 is placed at x = 4b. If Q2 has twice the charge of Q1, how much work is required to create this configuration, in terms of Q1, b, and the Coulomb constant, k?

Answer 1

W = 3/2 k q₁² / b

Step-by-step explanation:

Work is defined by

W = F . dx

Force is electric force

F = K q₁ q₂ / x²

W = k q₁ q₂ ∫ dx / x²

We integrate

W = k q₁ q₂ (-1 / x)

Evaluate from lower boundary x = b to upper boundary x = 4b

W = k q₁ q₂ (-1 / 4b + 1 / b)

Indicates that q₂ = 2q₁

W = k 2 q₁² 3/4b

W = 3/2 k q₁² / b