Two identical charged spheres are suspended by string of equal lengths. The string make an angle of 37° with each other. When suspended in a liquid of density 0.7 , the angle remains same. If density of material of the sphere is 1.4 , the dielectric const

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Solution

Q.
Two identical charged spheres are suspended by string of equal lengths. The string make an angle of 37° with each other. When suspended in a liquid of density 0.7 $g / {cm}^{3}$ , the angle remains same. If density of material of the sphere is 1.4 $g / {cm}^{3}$ , the dielectric constant of the liquid is $(\tan 37^{o} = \frac{3}{4})$ ______________ . [2024]

Ans.
(2)

$\tan θ = \frac{F_{e}}{m g}$ ...(1)

$\tan θ = \frac{F_{e} / K}{(m g - B)}$ ...(2)

$\frac{F_{e}}{K (m g - B)} = \frac{F_{e}}{m g}$

$K (m g - B) = m g$

$K (σ_{m} V g - ρ_{ℓ} V g) = σ_{m} V g$

$V k g [1.4 - 0.7] = 1.4 k g$

$K = \frac{1.4}{0.7} = 2$

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