An assembly of charges, +q, -q, +q, -q ........ are placed at distance x = 1m, x = 2m, x = 4m, x = 8m and so on, from the origin, in a plane. The potential at x = 0, due to the charges would be:
Correct answer: C. Finite and non-zero
- A. Zero
- B. Indeterminate
- C. Finite and non-zero
- D. Infinite
Explanation
The potential at any point due to a point charge is given by V = kq/r, where k is Coulomb's constant, q is the charge, and r is the distance from the charge to the point. In this problem, the charges are placed at distances that form a geometric progression: 1m, 2m, 4m, 8m, etc. The potential at the origin due to each charge will be V_n = k(-1)^n q/2^n. This forms an alternating geometric series. The series converges because the common ratio (1/2) is less than 1, resulting in a finite, non-zero potential. The alternating nature of the charges does not lead to cancellation because the terms decrease in magnitude, allowing for a finite sum.
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