Answer :
Final answer:
To calculate the electric field at the center of the square, we use the Coulomb's law formula for each charge located at the corners of the square. We then compute the vector sum of these electric fields, taking into account the direction of each field.
Explanation:
First, we use Coulomb's law formula to calculate the electric field created by a single charge, which is E = kQ/r², where E is the electric field, k is Coulomb's constant (8.99 x 10⁹ N.m²/C²), Q is the charge and r is the distance from the charge.
We calculate the electric field at the center of the square due to each charge separately. The electric field due to the -38.6 μC charge is E1 = kQ/r² = 8.99 x 10⁹ N.m²/C² * -38.6 x 10⁻⁶C/(0.425m/√2)², and similarly, the electric field due to each -27.0μC charge is E2 = kQ/r² = 8.99 x 10⁹ N.m²/C² * -27.0 x 10⁻⁶C/(0.425m/√2)².
The total electric field is simply the vector sum of the individual fields which would involve figuring out the geometric relationship between the individual electric fields. An important note is, electric fields from negative charges are directed towards the charges, so the directions of the fields must be taken into account while adding.
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