The work done by the electric field as the particle at corner P moves to infinity is -3k *q^2 / s.
To determine the work done by the electric field as the particle at corner P moves to infinity, we need to calculate the change in electric potential energy of the particle as it moves.
The electric potential energy of a charged particle in an electric field is given by:
U = qV
where U is the electric potential energy, q is the charge of the particle, and V is the electric potential at the particle's location.
The electric potential at a point due to a point charge is given by:
V = k * Q / r
where k is Coulomb's constant (8.98755 × 10^9 N·m^2·C^-2), Q is the charge of the point charge, and r is the distance between the point charge and the point where the potential is being evaluated.
In this case, we have three point charges, each with charge q. The distance between each point charge and the particle at corner P is s. Therefore, the total electric potential at corner P is:
V = 3k * q / s
The work done by the electric field as the particle at corner P moves to infinity is equal to the negative of the change in electric potential energy. Therefore, the work done is:
W = -ΔU = -q(3k * q / s) = -3k * q^2 / s .