Final answer:
To find the electric potential at the center of a square with charges at the corners, compute the potential due to each charge and add them up, taking into account that the potential due to a negative charge is negative.
Step-by-step explanation:
The electric potential at the center of a square due to point charges at its corners can be calculated using the formula for the potential due to a point charge: V = kQ/r, where V is the potential, k is Coulomb's constant (8.99 x 109 Nm2/C2), Q is the charge, and r is the distance from the charge to the point of interest. Since the potential is a scalar quantity, we can simply add the potentials due to individual charges at the center of the square.
For the charges Q, 2Q, -3Q, and 2Q, where Q = 6.1 µC and the side of the square is 8.0 cm, we first convert the side to meters: 8.0 cm = 0.08 m. The distance from each corner to the center in a square is \( \frac{s}{\sqrt{2}} \), where \( s \) is the side length. So, r = 0.08 m / \( \sqrt{2} \).
Calculating the potential at the center, we have:
Vtotal = VQ + V2Q + V-3Q + V2Q = k(Q/r + 2Q/r - 3Q/r + 2Q/r) = k(2Q/r),
So, substituting the values, we get:
Vtotal = 8.99 x 109 Nm2/C2 * (2 * 6.1 x 10-6 C) / (0.08 m / \( \sqrt{2} \)),
After computing, we find the electric potential at the center of the square due to these point charges.