Well, that sounds like an electrifying situation! Let's calculate the work done by the electric force.
To solve this problem, we can make use of the equation for the electric force:
F = k * (q1 * q2) / r^2
Where:
F is the electric force
k is the electrostatic constant (9 * 10^9 N m^2/C^2)
q1 and q2 are the charges (in this case, both are +3.0x10^-6 C)
r is the distance between the charges
Since the charges are fixed to diagonally opposite corners of a square, the distance between them is the length of the diagonal of the square, which can be calculated using the Pythagorean theorem:
d = sqrt((side length)^2 + (side length)^2)
Given that the side length of the square is 0.5 m, we can substitute this into the equation for d:
d = sqrt((0.5)^2 + (0.5)^2)
d = sqrt(0.5)
Now we can plug in the values into the equation for the electric force:
F = (9 * 10^9) * ((3.0x10^-6) * (3.0x10^-6)) / (0.5)
F = (9 * 10^9) * ((9.0x10^-12) / 0.5)
F = (9 * 10^9) * (1.8x10^-12)
F = 16.2x10^-3
Finally, we can calculate the work done by multiplying the force by the displacement:
Work = F * d
Work = (16.2x10^-3) * sqrt(0.5)
Work ≈ 11.49 J
So, approximately 11.49 Joules of work is done by the electric force as one of the charges moves to an empty corner.