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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

  • question_answer
        A thyroidal solenoid with an air core has an average radius of 15 cm, are of cross-section 12cm2 and 1200 turns. Ignoring the field variation across the cross-section of the toroid the self-inductance of the toroid is

    A)  4.6 mH                                

    B)  6.9 mH

    C)  2.3 mH                                

    D)  9.2 mH

    Correct Answer: C

    Solution :

                    For a solenoid, \[B={{\mu }_{0}}nI\] Where  \[n=\frac{N}{2\pi r}\] Flux linked with the solenoid is                 \[\phi =NBA\] \[\Rightarrow \]               \[\phi =\frac{{{\mu }_{0}}{{N}^{2}}IA}{2\pi r}\] \[\therefore \]  \[L=\frac{\phi }{I}=\frac{{{\mu }_{0}}{{N}^{2}}A}{2\pi r}\]                 \[4\pi \times {{10}^{-7}}\times {{(1200)}^{2}}\]                 \[=\frac{4\pi \times {{10}^{-3}}\times {{(1200)}^{2}}\times 12\times {{10}^{-4}}}{2\pi \times 15\times {{10}^{-2}}}\] \[L=2.3\times {{10}^{-3}}H=2.3\,mH\]


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