Answer to Question #102723 in Electricity and Magnetism for sridhar

Question

Two small spheres of each charge 'q' mass 'm and material density 'd' suspended from a fixed point with the help of inextensible light thread.When the spheres are in air the angle between the threads is 90°. When the spheres are suspended in a liquid of density 2d/3 the angle between the threads is 60°. The value of dielectric constant of the liquid is

Answer 1

$$\tan{\frac{90}{2}}=\frac{\frac{kq^2}{(2l\sin{\frac{90}{2}})^2}}{mg}$$

$$\tan{\frac{60}{2}}=\frac{\frac{kq^2}{(2l\sin{\frac{60}{2}})^2\epsilon}}{mg(1-\frac{2d}{3d})}$$

$$\epsilon=3\frac{\tan{45}\sin^2{45}}{\tan{30}\sin^2{30}}=10.392$$