Answer :
Final answer:
We calculate the electric field created by each corner charge at the center of the square, then calculate vector sum of these fields. We use the formula E = k|Q|/r², considering the distance from each corner to the center. The net electric field is found to be pointing towards the lower right from center due to the negative charges.
Explanation:
The problem asks us to calculate the electric field at the center of a square with one corner occupied by a -38.6 μC charge and the other three by -27.0 μC charges. To solve this, we utilize the formula E = k|Q|/r², where E is the electric field, k is Coulomb's constant, Q is the charge and r is the distance from the charge. Each corner charge creates an electric field at the center of the square. To find the net electric field, we calculate the electric field produced by each charge and then use vector addition for the resultant field.
Firstly, the distance from each corner to the center can be determined using the Pythagorean theorem, giving r = sqrt[(42.5cm / 2)² + (42.5cm / 2)²] = approximately 30.1cm. Then, applying the formula, we calculate the electric field at the middle of the square caused by the -38.6 μC charge and the three -27.0 μC charges separately. We add up these results and calculate their vector sum because the fields have different directions. Assuming the -38.6 μC charge is at the top left, the net electric field will point towards the lower right due to the negative charges.
By giving due attention to the direction of each field (which for negative charges is towards the charge), and assuming a coordinate system, we can resolve each of those fields into their x and y components. We can add the x-components together and the y-components together to find the total electric field using Pythagorean theorem and arctan for direction.
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