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(D) Given: Capacitance $C = 1 \mu F = 10^{-6} 	ext{ F}$.Spacing between the two spheres $d = r_2 - r_1 = 1 	ext{ mm} = 10^{-3} 	ext{ m}$.The formul

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$3 	ext{ m}$

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(D) Given: Capacitance $C = 1 \mu F = 10^{-6} 	ext{ F}$.Spacing between the two spheres $d = r_2 - r_1 = 1 	ext{ mm} = 10^{-3} 	ext{ m}$.The formula for the capacitance of a spherical capacitor is $C = 4 \pi \varepsilon_0 \frac{r_1 r_2}{r_2 - r_1}$.Substituting the values,we have $10^{-6} = \frac{1}{9 	imes 10^9} 	imes \frac{r_1 r_2}{10^{-3}}$.Since $r_1 = r_2 - 10^{-3}$,we get $9 	imes 10^3 = (r_2 - 10^{-3}) r_2$.$r_2^2 - 10^{-3} r_2 - 9 = 0$.Using the quadratic formula $r_2 = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$,we get $r_2 = \frac{10^{-3} \pm \sqrt{10^{-6} - 4(1)(-9)}}{2} = \frac{10^{-3} \pm \sqrt{36.000001}}{2} \approx \frac{6}{2} = 3 	ext{ m}$.

The capacitance of a spherical capacitor is $1 \mu F$. If the spacing between the two spheres is $1 \text{ mm}$,the radius of the outer sphere is

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