Neco 2022 Physics Question 8

Three point charges are placed at the vertices of a right‑angled triangle: \(Q_{1}=+2\ \mu\text{C}\) at \(A(0,0)\), \(Q_{2}=-3\ \mu\text{C}\) at \(B(4\ \text{m},0)\) and \(Q_{3}=+4\ \mu\text{C}\) at \(C(0,3\ \text{m})\). Let \(P\) be the midpoint of the hypotenuse \(BC\).\n\n(i) Find the magnitude (in N·C\(^{-1}\)) and direction (angle measured clockwise from the positive \(x\)-axis) of the resultant electric field at \(P\).\n\n(ii) A test charge \(q=+1\ \mu\text{C}\) is moved slowly from \(P\) to the point \(D\) on the altitude from \(A\) to \(BC\) (coordinates \(D(1.44\ \text{m},1.92\ \text{m})\)). Calculate the work done by an external agent in this process.