Subjects physics

Coulomb Potential Dfe91E

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1. The problem involves understanding the expression for the electric potential or force between charges using Coulomb's law, where $k = \frac{1}{4\pi\epsilon_0}$.\n\n2. The general formula for the potential due to point charges is $V = k \sum \frac{Q_i}{r_i}$, where $Q_i$ are charges and $r_i$ are distances from the point of interest.\n\n3. The options given are different combinations of charges $Q_1$, $Q_2$ and distances $r$, $R_1$, $R_2$. We need to identify which expression correctly represents the potential or force at a point.\n\n4. Option (1) is $k \frac{Q_1 + Q_2}{r}$, which assumes both charges are at the same distance $r$.\n\n5. Option (2) is $k \left( \frac{Q_1}{r} + \frac{Q_2}{R_2} \right)$, which sums potentials from charges at different distances.\n\n6. Option (3) is $k \left( \frac{Q_2}{r} + \frac{Q_1}{R_1} \right)$, similar to (2) but with charges swapped.\n\n7. Option (4) is $k \left( \frac{Q_1}{R_1} + \frac{Q_2}{R_2} \right)$, which sums potentials from both charges at their respective distances.\n\n8. Option (5) is 0, which would mean no potential or force.\n\n9. Without additional context, the most general and correct expression for the potential at a point due to two charges at distances $R_1$ and $R_2$ is option (4): $$V = k \left( \frac{Q_1}{R_1} + \frac{Q_2}{R_2} \right)$$\n\n10. This formula correctly sums the potentials from each charge at their respective distances, consistent with Coulomb's law.