Question

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle \(\theta\) with each other. When suspended in water the angle remains the same. If density of the material of the sphere is \(1.5\,g/cc,\) the dielectric constant of water will be ______

(Take density of water = 1 g/cc)

Answer 1

Correct answer is : 3

In air \(tan \frac {\theta}{2} = \frac {F}{mg} = \frac {q^2}{4 \pi\varepsilon _0 r^2mg}\)

In water \(tan \frac {\theta}{2}=\frac {F'}{mg'}=\frac {q^2}{4\pi \varepsilon _0 \varepsilon_1 r^2mg _{eff}}\)

Equate both equations

\(\varepsilon _0g=\varepsilon_0\varepsilon_rg \left[1-\frac {1}{1.5}\right]\)

\(\varepsilon_r = 3\)