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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

  • question_answer
        Two long conductors, separated by a distance d carry currents\[{{I}_{1}}\]and\[{{I}_{2}}\]in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3 d. The new value of the force between them is

    A)  \[-2F\]                                

    B)  \[F/3\]

    C)  \[-2F/3\]            

    D) \[-F/3\]

    Correct Answer: C

    Solution :

                    Force acting between two current carrying conductors \[F=\frac{{{\mu }_{0}}}{2\pi }\frac{{{I}_{1}}{{I}_{2}}}{d}l\]                             ?(i) where\[d=\]distance between the conductors, \[l=\]length of each conductor. Again     \[F=\frac{{{\mu }_{0}}}{2\pi }\frac{(-2{{I}_{1}})({{I}_{2}})}{(3d)}.l\]                 \[=-\frac{{{\mu }_{0}}}{2\pi }\frac{2{{I}_{1}}{{I}_{2}}}{3d}.l\]                                        ...(ii) Thus, from Eqs. (i) and (ii)                 \[\frac{F}{F}=-\frac{2}{3}\] \[\Rightarrow \]               \[F=-\frac{2}{3}F\]


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