Two equal positive point charges q are fixed at x=±a. A particle of charge -Q and mass m is constrained to move only along the y-axis near the origin. For small |y|, the force on it is approximately:
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Two equal positive point charges q are fixed at x=±a. A particle of charge -Q and mass m is constrained to move only along the y-axis near the origin. For small |y|, the force on it is approximately:

G1 Physics · Accepted Answer

The y-component of field due to both +q charges is E y = 2 [ k q E_y=2[kq E y ​ = 2 [ k q y/(a²+y²)^(3/2)] ≈ 2kq y/a³. The particle charge is -Q, so F y = − Q F_y=-Q F y ​ = − Q E y ≈ − 2 k q Q E_y≈-2kqQ E y ​ ≈ − 2 k q Q y/a³=-(2qQ/4πε₀a³)y.