Identical +3.07 µC charges are fixed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fixed to one of the empty corners, so that the total electric potential at the remaining empty corner is 0 V?

To solve this problem, we need to calculate the electric potential due to the two charges fixed to the adjacent corners of the square and then find the charge that should be fixed to one of the empty corners in order to make the total electric potential at the remaining empty corner equal to 0 V.

Let's break down the steps:

Step 1: Calculate the electric potential due to one of the charges at the remaining empty corner.
- The electric potential due to a point charge can be calculated using the formula V = k * q / r, where V is the electric potential, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the charge and the point where the electric potential is being calculated.
- In this case, the distance between one of the charges and the remaining empty corner is the length of the side of the square. Let's call it L.

So, the electric potential due to one charge at the remaining empty corner is V1 = k * q / L.

Step 2: Calculate the electric potential due to the other charge at the remaining empty corner.
- Since the charges are identical, the electric potential due to the other charge will be the same as the electric potential due to the first charge: V2 = V1.

Step 3: Calculate the net electric potential at the remaining empty corner.
- The net electric potential is simply the sum of the electric potentials due to the two charges: V_net = V1 + V2 = 2V1.

Step 4: Set the net electric potential to 0 V.
- In order for the net electric potential at the remaining empty corner to be 0 V, we need to set 2V1 equal to 0, which means V1 should be equal to 0.

Step 5: Solve for the charge, q.
- Substitute V1 = 0 into the equation V1 = k * q / L and solve for q:
0 = k * q / L.

Simplifying the equation:
0 = q / L.

Multiply both sides of the equation by L:
0 = q.

Therefore, the charge (magnitude and algebraic sign) that should be fixed to one of the empty corners is 0 C.

By fixing a charge of 0 C to one of the empty corners, the total electric potential at the remaining empty corner will be 0 V.