Question

two identical charged spheres are suspended in air by strings of equal lengths and make an angle of 30* with each other .when suapended in a liquid of density 0.8 g/cc., the angle remains the same . What is the dielectric constant of liquid ?Take density of the material of the sphere = 1.6 g/cc

Answer 1

this is based on concept of electrostatic
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if we split the component of Tension,
we see in equilibrium condition ,
Tcos15° = mg { virtical equilibrium

Tsin15° = Fs = KQ²/r² = Q²/4π€°r²
{ where r = 2lsin∅ , l is the length of string }

then,
tan15° = Q²/4π€°r²mg ------(1) initially

now, when , system submerged in liquid .

use Archenemies concept ,

Fnet{ downward in one string } = mg( 1-P/d)

where P is the density of liquid and d is the density of material

hence,
similarly ,

tan15° = Fs'/Fnet

tan15° = Q²/4π€mg(1-P/d) -------(2)

from eqn (1) and (2)

1/€° = 1/€(1 -P/d)

€° = €(1 - P/d )

€° = €° ×€' ( 1- P/d ) { here €' is actual dielectric constant of liquid }

€' = 1/( 1- P/d )

= 1/( 1- 0.8/1.6) = 2

hence , dielectric constant =2