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 g cm⁻³, the angle remains the same. If the density of the material of the sphere is 1.6 g cm⁻³, the dielectric constant of the liquid…

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 g cm⁻³, the angle remains the same. If the density of the material of the sphere is 1.6 g cm⁻³, the dielectric constant of the liquid is

Accepted Answer

(4) 2. In air, tan θ=F/(mg) with F=(kq²)/(x²). In the liquid two things change: the force becomes F/K, and the weight becomes the apparent weight mg(1-σ/ρ) because of buoyancy. The angle is unchanged, so F/(mg)=(F/K)/(mg(1-σ/ρ)), which gives K=ρ/(ρ-σ). K=(1.6)/(1.6-0.8)=(1.6)/(0.8)=2.

Step-by-step solution

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