Final answer:
The resultant electric potential at the center of a square with side √2 and point charges of 100 µC on each corner is 3596 V, which is not an option provided in the question.
Step-by-step explanation:
The student has asked about the electric potential at the center of a square with equal point charges on each of its corners. The charges are each 100 µC and are located at the corners of a square with sides of length √2. To find the resultant electric potential at the center of the square, we can use the formula for electric potential due to a point charge:
V = k * Q / r
Where V is the electric potential, k is Coulomb's constant (8.99 × 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the charge to the point in question. Each of the charges will contribute equally to the total potential at the center, and because electric potential is a scalar quantity, we simply add up the potential contributions from each charge.
The distance from the center of the square to any corner (r) is half the square's diagonal, which is √2 / √2 = √1 = 1 meter. Thus, the potential at the center due to one charge is:
V = (8.99 × 10^9 Nm^2/C^2) * (100 × 10^-6 C) / 1 m = 8.99 × 10^2 V
Since we have four charges, the total electric potential at the center is 4 times that amount, or V_total = 4 * 8.99 × 10^2 V = 3.596 × 10^3 V, which can be rounded to 3596 V. Thus, the given options do not contain the correct answer.