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Radii of two spheres forming a spherical condenser are 0.3 and 0.4m. If dielectric constant of medium is 4 and medium is completely filled in between, find the capacity of the condenser..

$\begin{array}{1 1} 5.34 \times 10^{-10}F \\ 4.43 \times 10^{-10}F \\ 4.66 \times 10^{-10}F\\ 1.74 \times 10^{-10}F \end{array}$

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  • If any dielectric is filled between two spheres, then the Capacity is given by C = $4 \pi \epsilon_o \large( \frac{Kab}{a-b})$, where K is the dielectric constant of the medium, and a and b are the radii of the concentric spheres, and $\epsilon_0$ is the permittivity of free space or electric constant.
Given $a = 0.4$ and $b = 0.3$, and $K = 4$, we need to calculate C.
We know that $\epsilon_0 =8.854 187 817... x 10^{−12} F/m$
$\Rightarrow C = 4 \pi \epsilon_o \large (\frac{Kab}{a-b})$$ = 4 \pi \times 8.854 187 817... x 10^{−12} \times \large\frac{4 \times \ 0.4 \times 0.3}{0.4 - 0.3}$
$\Rightarrow C = 5.34 \times 10^{-10} F$
answered Dec 20, 2013 by balaji.thirumalai

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