KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • 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 :

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

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