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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    A wire of fixed length is wound in such a way that it forms a solenoid of length \['\ell '\]and radius 'r'. Its self-inductance is found to be L. Now if same wire is wound in such a way that it forms a solenoid of length \[\frac{\ell }{2}\] and radius \[\frac{r}{2}\] then the self-inductance will be -

    A) 2L                   

    B) L   

    C) 4L                               

    D) 8L

    Correct Answer: A

    Solution :

    [A] \[L=\frac{{{\mu }_{0}}{{N}^{2}}\pi {{r}^{2}}}{\ell }\] length of wire\[=N\] \[2\pi r=\]Constant(=C, suppose) \[\therefore \,\,L={{\mu }_{0}}{{\left( \frac{C}{2\pi r} \right)}^{2}}\frac{\pi {{r}^{2}}}{\ell }\,\,\,\therefore L\propto \frac{1}{\ell }\] \[\therefore \]  Self inductance will become 2L.       


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