Question

A little charged bead is inside the hollow frictionless sphere manufactured from the insulating material. Sphere has a diameter of $50 \, cm$ . The mass of the bead is $90 \, mg$ , its charge is $0.5\text{ μC}$ . 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?

• A. $4.9\times 10^{- 8} \, C$
• B. $9.8\times 10^{- 8} \, C$
• C. $19.6\times 10^{- 8} \, C$
• D. $30.2\times 10^{- 8} \, C$

Answer 1

Answer: (B)

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 \alpha \geq \, mg \, sin ⁡ 2 \alpha $
then net force will be directed towards vertex i.e. initial equilibrium position
$\frac{k q Q}{d^{2}} \, sin \alpha \geq mg \, sin ⁡ 2 \alpha $
$d=diameter \, $ of sphere and $\text{ α }$ is very small
$\frac{k q Q}{d^{2}}\times \text{α }\geq \, mg \, \times \, 2\text{α}$
$Q \, \geq \, \frac{2 \, m g d^{2}}{K q}=9.8\times \, 10^{- 8} \, C$