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A spherical capacitor has a vacuum between its conducting shells and a capacitance of 125 pF. The outer shell has an inner radius of 9.00 cm. What is the outer radius of the inner shell?

Answer :

Final answer:

The question deals with the determination of the inner radius (a) of a spherical capacitor given its capacitance and the outer shell radius (b). Using the formula for the Capacitance of a spherical capacitor: a=b/(1+4πbC/4πε_0), the inner radius (a) is found to be approximately 8.99 cm.

Explanation:

The Capacitance(C) of a spherical capacitor is given by the formula C = 4πε_0*a*b / (b - a) where ε_0 is the permittivity of free space, a is the inner radius and b is the outer radius. We know the capacitance, permittivity of free space and the outer radius, and we need to find the inner radius.

Using the given values, we can rearrange the formula to solve for a: a = b / (1 + b*C / (4πε_0)).

Plugging in the given values (with capacitance in Farads, ε_0 = 8.8541*10^-12 F/m, b = 0.09m), we see that a = 0.09 / (1 + 0.09 * 125*10^-12 / (4*π*8.8541*10^-12)) which equals approximately 0.0899 m (or 8.99 cm). So, the outer radius of the inner shell is approximately 8.99 cm.

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