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Explanation:
Each ball is in equilibrium under following three forces:
i. tension, ii. electric force and iii. Weight
Lami's theorem can be applied
Where, K= dielectric constant of liquid and W' = W − upthrust Applying Lami's theorem in vacuum
W / sin(90∘ + θ) = Fe / sin(180∘ − θ)
Or W cos θ = Fe sinθ -------(1)
Similarly in liquid
W'/ (cos θ ) = Fe'/ (sin θ)
Dividing equation (1) by (2) we get.
W / W' = Fe/Fe'
K = W / (W - "upthrust")
(as Fe/Fe' = K) = (Vρg) / (Vρg - Vσg)
V = volume of ball) or
K = ρ / (ρ-σ )
Hence the dielectric constant for liquid is K = ρ / (ρ-σ )
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