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

  • question_answer
    A current of 1.5 A flows through a solenoid of length 20.0 cm, cross-section \[20.0\text{ }c{{m}^{2}}\] and 400 turns. The current is suddenly switched off in a short time of 1.0 millisecond. Ignoring the variation in the magnetic field the ends, the average back emf induced in the solenoid is:

    A) 0.3 V   

    B) 9.6 V

    C) 30.0 V  

    D) 3.0 V

    Correct Answer: A

    Solution :

    [a] \[{{e}_{back}}=L\frac{di}{dt}\]    where  \[L=\frac{{{\mu }_{0}}{{N}^{2}}A}{l}\] \[\therefore \,\,\,\,\,{{e}_{back}}=\frac{{{\mu }_{0}}{{N}^{2}}A}{l}\left[ \frac{1.5-0}{1\times {{10}^{3}}} \right]\] \[=\frac{4\pi \times {{10}^{-7}}{{(400)}^{2}}\times 20\times {{10}^{-4}}}{20\times {{10}^{-2}}}\times (1.5\times {{10}^{3}})\] = 0.3 V


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