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12th Class Physics Magnetism Question Bank MCQ - Moving Charges and Magnetism

  • question_answer
    Two long straight wires carrying the same current and separated by a distance r, exert force F per unit length on each other. If the current is decreased to l / 2 and separation between them is increased to 2r, then force will become:

    A) 8 F                   

    B) 2 F     

    C) F / 2                             

    D) F / 8

    Correct Answer: D

    Solution :

    (d) F / 8. It is given that \[{{l}_{1}}={{l}_{1}}=l\] \[\therefore \]      Force, \[F=\frac{{{\mu }_{0}}}{4\pi }\frac{2{{l}^{2}}}{r}\]      …(1) Now,     \[l'=l/2\] and \[r=2r\] So New force \[F;=\frac{{{\mu }_{0}}}{4\pi }\frac{2{{(l/2)}^{2}}}{2r}=\frac{{{\mu }_{0}}}{4\pi }\frac{2{{l}^{2}}}{8r}\]             \[=\frac{1}{8}\left( \frac{{{\mu }_{0}}}{4\pi }\frac{2{{l}^{2}}}{r} \right)=\frac{1}{8}F\]           (from eq. (1))


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