1. Concept: The electric potential at the direct surface of a charged conducting sphere behaves identically to a point charge mathematically located at the sphere's absolute center.
2. Formula: $$ V = \frac{k Q}{r} $$
3. Solution: - Given diameter = \( 2 \text{ cm} \). Therefore, radius \( r = 1 \text{ cm} = 0.01 \text{ m} = 10^{-2} \text{ m} \).
- Given charge \( Q = 1 \text{ mC} = 1 \times 10^{-3} \text{ C} \).
- Coulomb's constant \( k = 9 \times 10^9 \).
- Substitute: \( V = \frac{(9 \times 10^9) (1 \times 10^{-3})}{10^{-2}} \).
- Calculate numerator: \( 9 \times 10^6 \).
- Bring up the denominator's exponent: \( V = 9 \times 10^6 \times 10^2 = 9 \times 10^8 \text{ V} \).
- Convert to MegaVolts (\( 1 \text{ MV} = 10^6 \text{ V} \)): \( 900 \times 10^6 \text{ V} = 900 \text{ MV} \).
4. Why other options are incorrect: Options C and D mistakenly utilize the full 2cm diameter instead of halving it for the radius. Option B suffers from a massive scientific notation decimal error.
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