Four point charges qA = 2 mC, qB = –5 mC, qC = 2 mC, and qD = –5mC arelocated at the corners of a square ABCD of side 10 cm. What is theforce on a charge of 1 mC placed at the centre of the square?

To find the force on a charge of 1 mC placed at the center of the square, we can use the principle of superposition.

Step 1: Calculate the distance between the center of the square and each of the four charges. Since the square has sides of 10 cm, the distance from the center to any corner is half the length of the side, which is 5 cm.

Step 2: Calculate the electric force between the charge at the center and each of the four corner charges using Coulomb's law. Coulomb's law states that the force between two charges is given by the equation F = k * (q1 * q2) / r^2, where F is the force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

For qA and qC, the distance is 5 cm, so the force is F = (9 x 10^9 Nm^2/C^2) * ((2 mC * 1 mC) / (0.05 m)^2).

For qB and qD, the distance is also 5 cm, but the charges have opposite signs, so the force is negative: F = -(9 x 10^9 Nm^2/C^2) * ((5 mC * 1 mC) / (0.05 m)^2).

Step 3: Add up the forces from all four charges to find the net force on the charge at the center. Since the forces from qA and qC are in the same direction, and the forces from qB and qD are in the opposite direction, we can simplify the calculation by considering the magnitudes of the forces.

The magnitude of the force from qA and qC is the same, so we can add them: F_AC = 2 * F.

The magnitude of the force from qB and qD is also the same, but they have opposite signs, so we can subtract them: F_BD = -2 * F.

The net force on the charge at the center is then: F_net = F_AC + F_BD.

Step 4: Calculate the net force using the given values and perform the necessary calculations to find the final answer.

Please note that the final answer will depend on the specific values of the charges and the distance between them.