# Two identical balls each having density P are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now both the balls are immersed in liquid. As a result the angle does not change. the density of the liquid is sigma. find the dielectric constant of the liquid .

# Two identical balls each having density P are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now both the balls are immersed in liquid. As a result the angle does not change. the density of the liquid is sigma. find the dielectric constant of the liquid .

## 2 Answers

## Hence the dielectric constant for liquid is K = ρ / (ρ-σ )

**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 )