A conducting frame is placed in a horizontal plane as shown in the figure. The two sides are parallel and separated by a distance of 0.25 m. A massless conducting rod can slide without friction on the frame. The total resistance of the circuit is 40Ω. The rod is connected to a 0.2 kg mass by a massless cord which passes over a massless and frictionless pulley. An uniform magnetic field of 2T points vertically upward. The voltage of the battery is 100V. . Find the constant velocity 'v' in ms-1 with which the rod and mass eventually move.

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Accepted Answer

When the rod moves with constant velocity, net force on the bar is zero
$\begin{array}{l} ∴ W = gravitational force = mg = ilB \\ [i = induced current in the circuit] \\ ∴ i = \frac{0 .2 \times 10}{2 \times 0 .25} = 4 A \end{array}$
To produce 4A current in the bar, induced emf $ε$ in the circuit is $\frac{100 + ε}{40} = 4$
We know, $ε = BIV \Rightarrow V = \frac{ε}{Bl} = \frac{60}{2 \times 0 .25} = 120 {ms}^{- 1}$

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