Capacitor With Dielectrics: Practice Problem & Solution
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density \(0.8\text{ g cm}^{-3}\), the angle remains the same. If density of the material of the sphere is \(1.6\text{ g cm}^{-3}\), the dielectric constant of the liquid is :
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Capacitor With Dielectrics. Understanding the underlying formula is key to arriving at the correct answer below:
When the angle remains unchanged in a liquid, the dielectric constant is given by \(K = \frac{\rho}{\rho - \sigma}\), where \(\rho\) is density of sphere and \(\sigma\) is density of liquid. Thus, \(K = \frac{1.6}{1.6 - 0.8} = \frac{1.6}{0.8} = 2\).
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