Final answer:
The minimum work required to move the -.2 microcoulombs charge to infinity is calculated by summing the potential energies between this charge and the other two charges and then taking the negative of this value since work is done against the electric field.
Step-by-step explanation:
To calculate the minimum work required to move the first point charge to infinity, we assume the other two charges are fixed in place. The work required is equal to the change in potential energy as the charge moves from its initial position to infinity.
Step 1: Calculate the electrostatic potential energy U of the -.2 microcoulombs charge due to the other two charges. This can be given by the formula U = k * (q1*q2)/r, where k is Coulomb's constant (k = 8.988 × 10^9 N m²/C²), q1 and q2 are the charges, and r is the distance between them.
Step 2: Calculate the potential energy for each pair using the respective charge values and sum them up to find the total potential energy at the initial configuration.
When the charge has been moved to infinity, the potential energy due to that charge becomes zero because the distance r approaches infinity. Therefore, the work done in moving the charge to infinity is equal to the negative of the initial potential energy.
Let's proceed with the calculations.