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A charged conducting sphere is placed in a medium of permittivity $ε$ and resistivity $ρ$ . The sphere(capacitor) discharges through the surrounding medium with a time constant

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$ε ρ$

$ε / ρ$

$ρ / ε$

$ε^{2} ρ$

answer is A.

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Detailed Solution

The capacitance of the sphere is $4 π ε R$
The resistance of the medium is $\frac{ρ}{4 π R}$
Here R is the radius of the sphere. So the time constant $RC = ε ρ$

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