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 µC. What minimum charge must carry on 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 × 10^–8C
• B. 9.8 × 10^–8C
• C. 19.6 × 10^–8C
• D. 30.2 × 10^–8C

Answer 1

Answer: (B)

9.8 × 10^–8C

Answer 2

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 a ³ mg sin 2a. then net force will be directed toward vertex in initial equilibrium position

sin a ³ mg sin2 a

d-diameter of sphere and a is very small

× a ³ mg × 2 a

Q ³ $\frac { 2 \mathrm { mgd } ^ { 2 } } { \mathrm { kq } }$ = 9.8 × 10^–8 C