QJEEM24Ph5aba: JEE Main 2024 Physics - Class 12 JEEM24Ph5aba Solution: Two identical charged spheres are suspended by strings of equal …

Question

Verified Solution • 2025–26 Session moderate

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 \mathrm{~g} / \mathrm{cc}

, the dielectric constant of water will be __________.

(Take density of water

=1 \mathrm{~g} / \mathrm{cc}

)

Accepted Answer

In air

\tan \frac{\theta}{2}=\frac{F}{m g}=\frac{q^2}{4 \pi \varepsilon_0 r^2 m g}

In water

\tan \frac{\theta}{2}=\frac{\mathrm{F}^{\prime}}{\mathrm{mg}^{\prime}}=\frac{\mathrm{q}^2}{4 \pi \varepsilon_0 \varepsilon_{\mathrm{r}} \mathrm{r}^2 \mathrm{mg}_{\text {eff }}}

Equate both equations

\begin{aligned} ε_{0} g = ε_{0} ε_{r} g [1 - \frac{1}{1.5}] \\ ε_{r} = 3 \end{aligned}

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