The drawing shows six point charges arranged in a rectangle. The value of q is 8.07 μC, and the distance d is 0.430 m. Find the total electric potential at location P, which is at the center of the rectangle.

To find the total electric potential at location P, which is at the center of the rectangle, we need to calculate the electric potential due to each individual point charge and then add them up.

The electric potential due to a point charge at a distance r can be calculated using the formula:

V = k * q / r,

where V is the electric potential, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the location P.

In this case, we have six point charges arranged in a rectangle. Let's label them as follows:
A: Top left corner
B: Top right corner
C: Bottom right corner
D: Bottom left corner
E: Top center
F: Bottom center

First, let's calculate the electric potential due to charges A, B, C, and D. Since these charges are located on the corners of the rectangle, the distance between each of them and point P is d/√2 (using Pythagorean theorem).

V_ABCD = 4 * (k * q) / (d / √2)

Next, let's calculate the electric potential due to charges E and F. Since these charges are located at the centers of the top and bottom sides of the rectangle, the distance between each of them and point P is d/2.

V_EF = 2 * (k * q) / (d / 2)

Finally, we can find the total electric potential at point P by adding up the individual potentials:

V_total = V_ABCD + V_EF

Plugging in the given values of q (8.07 μC) and d (0.430 m) into the equation, and the value of Coulomb's constant (k = 9 x 10^9 Nm^2/C^2), you can calculate the total electric potential at point P.