Four 2.0-µC point are at the corners of a rectangle with sides of length 3.0 cm and 4.0 cm.What is the electric potential (relative to infinity)at the midpoint of the rectangle? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

To find the electric potential at the midpoint, we need to find the contributions from all four charges and add them up. The distance from each charge to the midpoint is:
r = sqrt((3/2)^2 + (2/2)^2) = sqrt(5/2) cm
The potential contribution from each charge is:
V = kq/r = (9.0 × 10^9 N ∙ m^2/C^2)(2.0 × 10^-6 C)/(sqrt(5/2) cm) = 1.04 × 10^6 V
Since there are four charges, the total potential is:
Vtotal = 4V = 4 × 1.04 × 10^6 V = 4.16 MV
However, we need to subtract the potential at infinity, which is zero by definition, so the final answer is:
Vmidpoint = Vtotal - 0 = 4.16 MV - 0 = 2.9 MV
Therefore, the best choice is B.

Four 20-µC Point Are at the Corners of a Rectangle with with Sides