Figure shows two long metal rails placed horizontally and parallel to each other at a separation l. A uniform magnetic field B exists in the vertically downward direction. A wire of mass m can slide on the rails. The rails are connected to a constant current source which drives a current i in the circuit. The friction coefficient between the rails  and the wire is µ  . What should be the minimum value of µ  which can prevent the wire from sliding on the rails? 

Figure shows two long metal rails placed horizontally and parallel to each other at a separation l. A uniform magnetic field B exists in the vertically downward direction. A wire of mass m can slide on the rails. The rails are connected to a constant current source which drives a current i in the circuit. The friction coefficient between the rails  and the wire is µ  . What should be the minimum value of µ  which can prevent the wire from sliding on the rails?
 

  1. A

    ilBmg

  2. B

    2ilBmg

  3. C

    3ilBmg

  4. D

    4ilBmg

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    Solution:

    The force on the wire due to the magnetic field is F=il×B
    Or, F=ilB
    It acts towards right in the given figure. If the wire does not slide on the rails, the force of friction by the rails should be equal to F. If μ0 be the minimum coefficient of friction which can prevent sliding, this force is also equal to μ0  mg. Thus,
    μ0mg=ilB  Or ,μ0=ilBmg

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