Problem 1. As observed in lectures, one of the most important types of vector elds in physics and engineering is the electric eld E. If we place an electric charge at the point m0 = (x0, yo, 20) in space, it generates a vector force eld E (ac, y, 2) given by: ; q 117on yyo ZZO E _ (m,y,Z) 471750 , where q is the electric charge, and 80 is a constant representing the permittivity of air, and |m| represents the magnitude of the vector cc, i,e., |:1:| = x/x2+y2+22. (sometimes, the magnitude is denoted by ||.||, that is, ||:1:|| = V1132 + 212 +22). a) Prove that E is a conservative force eld With the potential energy: _ q U($ayaz)_47r0|$_m0|a in the sense E = VU. b) Two electric charges, q and q, are located at the points (1,0,0) and (1,(),0), respectively. Find the electric eld E and the associated potential energy U at an arbitrary point (:13, y, 2) that is not (1,0,0) or (1, 0,0). The electric eld and potential energy follow the principle of superposition, where they result from the addition of two elds and potentials