Question

Find the minimum surface density of charge on the plate, so that a body of mass 2 kg/m2 may just be lifted.

Answer 1

Let minimum surface charge density = σ C/m²
Let mass per unit area = m = 2 kg/m²

We know, force per unit area act on the plate = σ²/2∈₀
∴ σ²/2∈₀ = mg
⇒ σ² = 2mg∈₀
⇒σ² = 2 × 2 × 10 × 8.85 × 10⁻¹² kg²/m⁴
taking square root both sides,
σ = 18.8 × 10⁻⁶ kg/m²

Hence, surface charge density = 1.88 × 10⁻⁵ kg/m²