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As shown in the figure, a conducting rod...

As shown in the figure, a conducting rod of length I, mass m and resistance R falls through a magnetic field `vecB` in a plane perpendicular to plane of figure. Find terminal velocity of rod.

Text Solution

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When velocity of the rod is v, the induced emf in the rod =Bvl (-sign neglected) ,
`therefore` Induced current in rod =`I=(Bvl)/R`…(1)
The force acting on the rod is in opposite direction
`F_B=I lB`
Substituting the value of (I) from equation (1),
`F_B=(B^2vl^2)/R` ...(2)
When the force becomes equal to the weight of the rod , acceleration of the rod will become zero and the rod continues to move with constant (terminal ) velocity `(v_t)`.
`therefore mg=(B^2v_t l^2)/R`
`therefore v_t=(mgR)/(B^2l^2)`
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