Question

A point charge of q is placed at the center of a square. when a second point charge of -q is placed at one of the square's corners, it is observed that an electrostatic force of 2 n acts on the positive charge at the square's center. next, identical charges of -q are placed at the other three corners of the square. what is the magnitude of the electrostatic force acting on the positive charge at the center of the square?

Answer 1

The magnitude of the electrostatic force acting on the positive charge at the center of the square when all four charges are placed at the corners is zero.

Step-by-step explanation:

The electrostatic force on the positive charge at the center of the square can be calculated by summing the individual forces exerted by each of the four charges placed at the corners of the square. Since the charges at the bottom left and top right corners are positive and have the same magnitude as the charge at the center, they will repel the charge at the center.

On the other hand, the charges at the bottom right and top left corners are negative and also have the same magnitude, so they will attract the charge at the center.

Using Coulomb's law, the magnitude of the electrostatic force between two charges is given by the equation F = k|q1q2|/r^2, where F is the force, q1 and q2 are the magnitudes of the charges, k is Coulomb's constant (9.0 x 10^9 N m^2/C^2), and r is the distance between the charges.

Since the charges at the bottom right and top left corners are -q, the force they exert on the charge at the center is -2kq^2/r^2. The charges at the bottom left and top right corners, which are +q, exert a force of +2kq^2/r^2 on the charge at the center. Therefore, the total force exerted on the charge at the center is (-2kq^2/r^2) + (-2kq^2/r^2) + (2kq^2/r^2) + (2kq^2/r^2) = 0, meaning that there is no net electrostatic force on the charge at the center when the other three charges are placed at the corners of the square.