Question

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of q and a? Express your answer in terms of the variables q, a, constant k, and appropriate constants.

Answer 1

The magnitude of the net electric field at the center of a square with charges at its corners is determined using Coulomb's Law and is given by E_net = 2√2k|q|/a^2, directed vertically.

Step-by-step explanation:

The magnitude of the net electric field at the center of a square due to four point charges located at its corners can be determined using Coulomb's Law, which states that the electric field E due to a point charge Q is given by E = k|Q|/r2, where k is Coulomb's constant, and r is the distance from the charge to the point of interest. For a square of side length a, the distance from any corner to the center is a/√2. If opposite charges are equal in magnitude but opposite in sign, their fields at the center will cancel in the horizontal direction and add up in the vertical direction. Hence, the net field will be directed either straight up or straight down depending on the sign of the charges, with the magnitude of the net electric field given by Enet = 2k|q|/(a/√2)2 = 2√2k|q|/a2.