A little charged bead is inside the hollow frictionless sphere manufactured from the insulating material. Sphere has a diameter of 50 c m . The mass of the bead is 90 m g , its charge is 0.5 μC . What minimum charge must carry an object at the bottom of the sphere to keep hold the charged bead at the vertex of the sphere in stable equilibrium?

Step-by-step solution

Let give small displacement to q . The equilibrium will be stable if net force after giving displacement will be in direction of position of equilibrium F e sin ⁡ α ≥ m g sin ⁡ 2 α then net force will be directed towards vertex i.e. initial equilibrium position k q Q d 2 sin ⁡ α ≥ m g sin ⁡ 2 α d = d i a m e t e r of sphere and α is very small k q Q d 2 × α ≥ m g × 2 α Q ≥ 2 m g d 2 K q = 9.8 × 10 - 8 C