One insulated conductor from a household extension cord has a mass per unit length of $μ.$ A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the  length of the cord. When the cord carries an $AC$ current of $"i"$ at a frequency of $f,$ it  vibrates in resonance in its simplest standing-wave vibration state. Determine the  relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.

  • A

    $T=4\mu f^2d^2$

  • B

    $T=2\mu f^2d^2$

  • C

    $T=\frac{\mu f^2d^2}{2}$

  • D

    $T=\frac{\mu f^2d^2}{4}$

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