Question

A particle of mass 5 x 10⁻⁹ kg is held at some distance from very large uniformly charged plane. The surface charge density on the plane is 4 x 10⁻⁶C/m². What should be the charge on the particle so that the particle remains stationary even after releasing it ?
ε₀ = 8.85 x 10⁻¹² C⁻² m², g = 9.8 ms⁻²

Answer 1

Dear Student,

◆ Answer -

q = 2.168×10^-13 C

◆ Explanation -

For the particle to remain stationary, its gravitational force should be balanced by electrostatic force.

Fg = Fe

m.g = q.E

m.g = q.σ/2ε₀

q = 2m.g.ε₀/σ

Substitute values,

q = 2 × 5×10^-9 × 9.8 × 8.85×10^-12 / 4×10^-6

q = 2.168×10^-13 C

Therefore, charge on the particle must be 2.168×10^-13 C.

Hope this helps you...