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 \[{{V}_{B}}-{{V}_{A}}=-\,\,({{V}_{C}}-{{V}_{B}})\] |
\[\therefore as\,\,{{W}_{AB}}=-\,{{W}_{BC}}\] |
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