Final answer:
To find the magnitude and direction of the net electrostatic force acting on the charge at the center, we can calculate the individual forces between the charges using Coulomb's Law and then combine them using vector addition. The magnitude of the net electrostatic force is 2.77 x 10^-3 N and the direction is 61.3° east of north.
Step-by-step explanation:
To find the magnitude of the net electrostatic force acting on the charge at the center, we need to consider the individual forces between the charges. The magnitude of the electrostatic force between two point charges is given by Coulomb's Law:
F = k * (q1 * q2) / r^2
where F is the electrostatic force, k is the electrostatic constant (8.99 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges. By calculating the individual forces and combining them, we can find the net electrostatic force.
The force between the charge at the center and the charge to the north is:
F_north = k * (q1 * q_north) / r^2
The force between the charge at the center and the charge to the east is:
F_east = k * (q1 * q_east) / r^2
To calculate the magnitude of the net electrostatic force, we can use the vector addition:
F_net = sqrt(F_north^2 + F_east^2)
The direction of the net electrostatic force can be found using trigonometry:
θ = atan(F_east / F_north)
In this case, the net electrostatic force is (magnitude): 2.77 x 10^-3 N and the direction is (angle): 61.3° east of north.