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I came across a question which states:

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is . The spheres are now immersed in a dielectric liquid of density 800 $\frac{kg}{m^3}$ and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

(A) electric force between the spheres remains unchanged

(B) electric force between the spheres reduces

(Source IIT JEE Advanced 2020)

In my opinion, the first option should be correct because the electric force between the charged spheres will remain constant and equal to $F = \frac{Q_1Q_2}{4\pi\epsilon_0r^2}$ $\space$ but the answer given by the organizers is the second option (that is, the B option). Can anybody tell where am I going wrong in this question?

ecneics
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2 Answers2

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It is difficult to deal with forces between objects immersed in a fluid because the electric field can attract the fluid into high field regions and this affects the fluid pressure. To answer need to compute the full stress tensor which involves both the electric and mechanical forces. I think that the author (of what sounds like an introductory textbook problem) is blisfully unaware that there is no simple answer to his problem.

mike stone
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If the charge distribution remains spherical, the electric displacement vector field created by a charge is $\vec{D}=\frac{Q}{4\pi r^2}\vec{e_r}$ and the electric field $ \vec{E}=\frac{\vec{D}}{\epsilon_0\epsilon_r}=\frac{Q}{4\pi{\epsilon_0\epsilon_rr}^2}\vec{e_r}$

The force on the other charge is therefore divided by $\epsilon_r$

Vincent Fraticelli
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