Electrostatics Question 1
Question 1 - 2024 (01 Feb Shift 1)
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 $=1 g / cc$ )
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Answer: (3)
In air $\tan \frac{\theta}{2}=\frac{F}{mg}=\frac{q^{2}}{4 \pi \varepsilon _0 r^{2} mg}$
In water $\tan \frac{\theta}{2}=\frac{F^{\prime}}{mg^{\prime}}=\frac{q^{2}}{4 \pi \varepsilon _0 \varepsilon _r r^{2} mg _{\text {eff }}}$
Equate both equations
$\varepsilon _0 g=\varepsilon _0 \varepsilon _r g\left[1-\frac{1}{1.5}\right]$
$\varepsilon _r=3$
