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Question:

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8 gcm⁻³, the angle remains the same. If the density of the material of the sphere is 1.6 gcm⁻³, the dielectric constant of the liquid is:

2

1

4

3

Solution:

From fig, tanθ = qE/mg
tan15° = kq²/d²mg
tan15° = kq²/1.6Vgd² [V is the volume].. (1)
When system is suspended in liquid,
tan15° = kq²/K(mg - ρVg)d²
tan15° = kq²/K(1.6 - 0.8)Vgd² (2)
from (1) and (2) we get,
kq²/K(1.6 - 0.8)Vgd² = kq²/1.6Vgd²
∴K = 2
Dielectric constant of liquid = 2