1. Concept: A spherical capacitor consists of two concentric conducting spheres of radii \( a \) (inner) and \( b \) (outer).
2. Formula: $$ C = \frac{Q}{\Delta V} = \frac{4 \pi \epsilon_0}{\frac{1}{a} - \frac{1}{b}} $$
3. Solution: - The potential difference between the spheres is \( \Delta V = \frac{Q}{4 \pi \epsilon_0} \left(\frac{1}{a} - \frac{1}{b}\right) \).
- Find a common denominator for the radius terms: \( \left(\frac{b - a}{ab}\right) \).
- Inverting this when dividing \( Q \) by \( \Delta V \) shifts \( ab \) to the numerator, resulting in \( C = 4 \pi \epsilon_0 \left(\frac{ab}{b-a}\right) \).
4. Why other options are incorrect: The other options fail to account for the reciprocal geometric derivation resulting from the point-charge potential formula.
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