Two identical thin metal plates having charges q₁ and q₂ are brought close to each other to form a parallel plate capacitor of plate area A . The magnitude of the net electrostatic force experienced by one of the plates is :

Step-by-step solution

The electric field produced by plate 2 at the location of plate 1 is uniform and has a magnitude E₂ = q₂ 2A ₀ . Since plate 1 has a total charge q₁ and sits entirely in this uniform field, the net force on it is F = q₁ E₂ = q₁ q₂ 2A ₀ . Alternatively, the charge on the outer surfaces of the plates is q₁ + q₂ 2 and on the inner surfaces is q₁ - q₂ 2 . The outward force on the outer surface is F_ out = ( q₁ + q₂ 2 )^2 2A ₀ . The inward force on the inner surface is F_ in = ( q₁ - q₂ 2 )^2 2A ₀ . The net force is F =