The space between two concentric conducting spherical shells of radius a and 2a is filled with a dielectic medium having dielectric constant K and resistivity $ρ$ . The inner sphere is given a charge $+ Q$ at $t = 0$ and outer is earthed then

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charge on inner sphere as a function of time is $Q e^{- \frac{2 t}{e_{0} K_{ρ}}}$

resistance is $\frac{ρ}{8 a}$

resistance is $\frac{ρ}{4 a}$

charge on inner sphere as a function of time is $Q e^{- \frac{t}{ε_{0} K_{ρ}}}$

answer is A.

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Detailed Solution

$q = Q e^{- t / R C} R = \frac{f}{8 π a} C = \frac{4 π ε_{0} k \times 2 a}{8 π ε_{0} k} \Rightarrow R C = p ε_{0} k S o q = Q e^{- \frac{t}{p ε_{0} k}}$

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