Physics · Electrostatic Potential And Capacitance · NEET
It is a SCALAR. Energy has no direction, so you just add the pair terms with their signs (+ or -). You never break U into x and y components. This is why questions on system PE are usually faster than force questions - no vector addition, just add numbers with correct signs.
U comes from bringing charges one at a time. The first charge needs no work (empty space). When you bring the second, you do work in the field of the first - that gives one q1q2 term. Bringing the third gives a q1q3 term and a q2q3 term. So each pair appears exactly once. For n charges the number of pair terms is n(n-1)/2: 3 charges give 3 terms, 4 charges give 6 terms.
Look at the product qi qj for each pair. If qi qj > 0 (like charges, both + or both -), that term is POSITIVE (you did positive work against repulsion). If qi qj < 0 (unlike charges), that term is NEGATIVE (the attraction helped you). The total U can be positive, negative, or zero depending on which pairs dominate.
No. Because the electrostatic force is conservative, work is path-independent AND order-independent. Whether you bring q1 first or q2 first, the final U is the same. So you can assemble the system in any order and always add the same set of pair terms.
U of a SYSTEM (this page) uses only the charges you are given - they create each other's fields, so U = sum of k qi qj / rij. U of a single charge in an EXTERNAL field (next topic) uses U = qV, where V is made by outside sources, not by the charge itself. Do not mix the two: system PE never has a lone qV term.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
U = k q1 q2 / r, where k = 1/(4 pi epsilon0) = 9 x 10^9 N m^2/C^2, and r is the distance between them. The signs of q1 and q2 are kept inside the product.
The joule (J), the same as any energy. In sub-questions charges are often in microcoulomb (10^-6 C) and distances in cm (10^-2 m), so convert before substituting.
Six. The number of pairs for n charges is n(n-1)/2, so 4 x 3 / 2 = 6 terms, each of the form k qi qj / rij.
Yes. The total external work done to bring the charges from infinity to their positions (slowly, no kinetic energy) equals the stored potential energy U of the system.
It tests whether you can count pairs correctly and handle signs - both common trap points. It also links to energy conservation problems where a charge is released and gains kinetic energy equal to the drop in U.
