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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2011

  • question_answer
    What is the magnitude of the emf generated between the ends of the axle of a railway carriage 1 m in length when it is moving with a velocity of 30 km/h along horizontal track? Earth's horizontal magnetic field of induction\[=0.4\times {{10}^{-4}}T\]and angle of dip \[=60{}^\circ \]

    A)  \[6.77\times {{10}^{-4}}V\]    

    B)  \[5.77\times {{10}^{-4}}V\]

    C)  \[5.23\times {{10}^{-4}}V\]    

    D)  \[5.47\times {{10}^{-4}}V\]

    Correct Answer: B

    Solution :

     The earth's horizontal magnetic induction component is given by \[{{B}_{H}}=B\,cos\,60{}^\circ \] \[B=\frac{{{B}_{H}}}{\cos 60{}^\circ }\] \[B=\frac{0.4\times {{10}^{-4}}}{1/2}=0.8\times {{10}^{-4}}T\] and the vertical component of B \[{{B}_{V}}=B\text{ }sin\text{ }60{}^\circ =0.8\times {{10}^{-4}}\times \frac{\sqrt{3}}{2}\] The emf induced \[E=BLv\] \[=0.8\times {{10}^{-4}}\times \frac{\sqrt{3}}{2}\times 1\times 30\times \frac{5}{18}\] \[=5.77\times {{10}^{-4}}V\]


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