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) \[{{W}_{AB}}=0\]

Correct Answer: B

Solution :

[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 \[{{V}_{B}}-{{V}_{A}}=-\,\,({{V}_{C}}-{{V}_{B}})\]

\[\therefore as\,\,{{W}_{AB}}=-\,{{W}_{BC}}\]