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JEE Main & Advanced Physics Electro Magnetic Induction Question Bank Self Evaluation Test - Electromagnetic Induction

  • question_answer
    A wire of fixed lengths is wound on a solenoid of length \[\ell \] and radius r. Its self-inductance is found to be L. Now if same wire is wound on a solenoid of length \[\ell /2\] and radius r/2, then the self in- ductance 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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