A spherical-shaped capacitor has a charge equivalent to 4.45 nanocoulombs when connected to a battery that has a voltage of 220 V. Suppose the two shells of the spherical capacitor are 5.34 centimeters apart, what are the capacitance and the radius of the inner sphere?
The capacitance is given by
"C=\\frac{q}{V}=\\frac{4.45*10^{-9}}{220}=2.02*10^{-11}\\:\\rm F"On the other hand
"C=4\\pi\\epsilon_0(R_2*R_1)\/(R_2-R_1)""R_2=R_1+0.0534"So
"2.02*10^{-11}=3.14*8.85*10^{-12}\\frac{(R_1+0.0534)R_1}{0.0534}""(R_1+0.0534)R_1=0.0389"
"R_1=0.172\\:\\rm m"
"R_2=0.226\\:\\rm m"
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