Question

calculate the electric field at the center of a square 42.5 cm on a side if one corner is occupied by a -33.8 mc charge and the other three are occupied by -22.0 mc charges.

Answer 1

To calculate the electric field at the center of the square, we need to find the individual electric fields generated by each charge at that point and then add them vectorially. The electric field due to a point charge can be calculated using Coulomb's law:

Electric field (E) = (k * q) / r^2

where k is the electrostatic constant (9 × 10^9 Nm^2/C^2), q is the charge, and r is the distance between the charge and the point where we want to calculate the electric field.

Let's calculate the electric field due to each charge:

1. For the charge of -33.8 mc at one corner: Since the corner charge is at a diagonal corner, the distance to the center is given by d1 = √(42.5 cm)^2 + (42.5 cm)^2.

Using Coulomb's law, the electric field due to this charge is:

E1 = (9 × 10^9 Nm^2/C^2) * (-33.8 × 10^(-6) C) / (d1)^2

2- For the charges of -22.0 mc at the other three corners:

Since the other charges are at the three remaining corners, the distance to the center is given by d2 = 42.5 cm.

Using Coulomb's law, the electric field due to each charge is:

E2 = (9 × 10^9 Nm^2/C^2) * (-22.0 × 10^(-6) C) / (d2)^2

To find the total electric field at the center, we need to sum up the individual electric fields:

E_total = E1 + E2 + E2 + E2

Note that we are adding E2 three times because there are three charges with the same magnitude at the remaining corners.

Perform the calculations with the given values to find the electric field at the center of the square.