1. Concept: Electric potential is a scalar quantity. The total potential is zero where the positive potential from \( Q_1 \) exactly cancels the negative potential from \( Q_2 \).
2. Formula: $$ V_{total} = \frac{k Q_1}{r_1} + \frac{k Q_2}{r_2} = 0 $$
3. Solution: - Let the point be at distance \( x \) from \( Q_1 \). The distance from \( Q_2 \) is \( (100 - x) \).
- Set up the equation: \( \frac{k (3\mu\text{C})}{x} + \frac{k (-1\mu\text{C})}{100 - x} = 0 \).
- Rearrange: \( \frac{3}{x} = \frac{1}{100 - x} \).
- Cross-multiply: \( 3(100 - x) = x \implies 300 - 3x = x \implies 4x = 300 \).
- Solve for \( x \): \( x = 75 \text{ cm} \) from \( Q_1 \).
- The distance from \( Q_2 \) is \( 100 - 75 = 25 \text{ cm} \).
4. Why other options are incorrect: Option B is the distance from \( Q_1 \), not \( Q_2 \). Options C and D result from mathematical setup errors or averaging the distances.
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