• # question_answer Three point A, B & C are at a distance of 1 m, 2 m & 1 m from an infinitely long charged wire of linear charge density $\lambda \,\,C/m.$ A charge q is taken from A to B, B to C and finally C to A. Which of the following is/are correct about the work done in the above process - A) ${{W}_{AB}}=2\,\,{{W}_{BC}}$                    B) ${{W}_{AB}}=-\,{{W}_{BC}}$ C) ${{W}_{BC}}=0$                    D) ${{W}_{AB}}=0$

[B]  Work done to move change q from A to B $={{W}_{AB}}=q\,\,({{V}_{B}}-{{V}_{A}})$ ${{W}_{AB}}=q\,\,({{V}_{B}}-{{V}_{A}})$ Work done to move charge q from B to C $={{W}_{BC}}=q\,\,({{V}_{C}}-{{V}_{B}})$ ${{W}_{BC}}=q\,\,({{V}_{C}}-{{V}_{B}})$ ${{V}_{B}}-{{V}_{A}}=\frac{-\lambda }{2\pi {{\in }_{0}}}\text{ln}\,\,2,$ ${{V}_{C}}-{{V}_{B}}=\frac{-\lambda }{2\pi {{\in }_{0}}}\text{ln}\,\,2$ as ${{V}_{B}}-{{V}_{A}}=-\,\,({{V}_{C}}-{{V}_{B}})$ $\therefore as\,\,{{W}_{AB}}=-\,{{W}_{BC}}$