Question

Using the symmetry of the arrangement, show that the net Coulomb force on the charge q at the center of the square below (Figure 18.40) is zero if the charges on the four corners are exactly equal.

a) True
b) False

Answer 1

The net Coulomb force on a charge at the center of a square with equal corner charges is zero due to symmetrical arrangement, with forces from opposite corners canceling each other out.

Step-by-step explanation:

The question is asking to demonstrate why the net Coulomb force on a charge located at the center of a square with equal charges on the corners is zero. By the principle of superposition, the total electric force on a charge is the vector sum of the individual forces exerted by each charge present. Here, we have a symmetrical arrangement with equal charges located at each corner of the square. The forces exerted by diagonally opposite charges on the central charge will be equal in magnitude but opposite in direction, thereby canceling each other out. Hence, due to symmetry, the forces from each corner on the central charge will be balanced, and the net force on the central charge will be zero.