Four point charges q1 = 42 = 3 = q4 = q, with q = 3 × 10-º C, are placed on the vertex of a square as shown in

Figure 1. The square side is 2a = 5 m. Derive the expression for the electric field generated by q1, 92 and q3at the coordinates of the charge q4, function of the parameters q and[3]а. Derive the expression of the force exerted by the charges q1, 92 and q3on the charge q4, function of the parameters q and a.[2] Calculate the magnitude and direction of the force exerted by thecharges q1, q2 and q3 on the charge q4.[2] Derive the expression for the scalar potential in a generic point xo onthe x axis, that is, a point with coordinates (xo, 0, 0), function of qand a.[6] Calculate the value of the scalar potential at a coordinate x = 1 m on[2]the x axis. Derive the expression for the electric field in the x direction, along the x axis, function of the parameters a, q and of the coordinate x.[4] Calculate the magnitude of the x-component of the electric field at x = 2 m.[2] Calculate the kinetic and potential energy that an electron left free to move at a point P of coordinates (2 a; 0; 0) with initial zero velocity acquires when it reaches the point with coordinates (-2 a; 0; 0).[4]