Two identical charged spheres are suspended by strings of equal lengths The string makes an angle of 30 with - Physics - Electric Charges and Fields

Question

Two identical charged spheres are suspended by strings of
equal lengths The string makes an angle of 30 with each other When
suspended in liquid of density 0 8g/cm^3, The angle remains the
same if density of material of sphere is 1 6g/cm^3 the dielectric
constant of liquid is?

Vaibhav T. · Accepted Answer

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Suppose T is the tension in the string Force of repulsion
F=14πε0×q2r2
Resolving these forces in the horizontal and vertical components as
shown in figure
Tcosθ=mgTsinθ=14πε0×q2r2Dividing we
get , tanθ=q24πε0mgr2 ---(1)On immersing in the
liquid,Appearent weight mg' =mg1-0 81 6=mg2Force of repulsion F' =
14πε0K×q2r2If T' is the new tension ,then
T'cosθ=mg2T'sinθ=q24πε0Kr2Dividing :
tanθ=2q24πε0Kmgr2Using (1)
2q24πε0Kmgr2=q24πε0mgr2 K=2

Dielectric constant of liquid is 2

Two identical charged spheres are suspended by strings of equal lengths .The string makes an angle of 30 with each other When suspended in liquid of density 0.8g/cm^3, The angle remains the same.if density of material of sphere is 1.6g/cm^3 the dielectric constant of liquid is?