Final answer:
To determine the electric field at the center of the rectangle, we use the principle of superposition and consider only the vertical components of the fields due to the symmetry. Coulomb's law governs the force between a center charge and one of the corner charges. An attractive force exists between the -5Q charge at the center and a +2Q corner charge.
Step-by-step explanation:
To calculate the magnitude and direction of the electric field at the center of the rectangle due to the four point charges, we need to use the principle of superposition, which states that the total electric field caused by multiple charges is the vector sum of the electric fields produced by each charge individually. Let's denote the electric field due to a single charge as E, which can be calculated using Coulomb's law: E = k * |q| / r^2, where k is Coulomb's constant, q is the charge, and r is the distance from the charge to the point of interest.
The charges are symmetrically placed so the horizontal components of the electric fields due to the charges will cancel each other out. Thus, we only need to consider the vertical components of the electric fields due to the charges. By calculating the vertical components of the electric fields for either the top two charges or the bottom two charges and doubling the result, we can find the total electric field at the center of the rectangle.
The law that governs the force between the charge at the center and one of the +2Q charges is Coulomb's law, which states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Coulomb's law can be written as F = k * |q1 * q2| / r^2. The magnitude of the force will thus be calculated using the values of -5Q and +2Q for the charges and the distance from the center to a corner charge.
The type of force will be attractive since the charges have opposite signs.