The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot?
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1
Identify the charges on the two halves of the rod. One half is positively charged (+Q) and the other half is negatively charged (-Q).
Consider the symmetry of the problem. The point where the electric potential is to be calculated is equidistant from both halves of the rod. This symmetry will simplify the calculation.
Use the formula for the electric potential due to a point charge, V = k \frac{Q}{r}, where V is the potential, k is Coulomb's constant, Q is the charge, and r is the distance from the charge to the point of interest.
Calculate the contributions to the electric potential at the point from each half of the rod separately, considering their respective distances from the point.
Sum the contributions from both halves of the rod to find the total electric potential at the point. Due to the opposite signs of the charges and the symmetry of the setup, the contributions may partially or fully cancel each other out.