A conducting rod of length 2m having uniform resistance per unit length $2 Ω / m$ , is moving with constant velocity of 4m/s on two smooth, resistance less parallel rails in horizontal plane. A $9 Ω$ resistor is connected to the ends of rails as shown. There exist a uniform magnetic field $B_{0} = 2 T$ entering into the plane of paper. The potential difference between the ends of the rod during motion is 13V. The separation between the rails is $\frac{N}{6} m$ , where N = ___

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answer is 9.

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Detailed Solution

$v = ε - i R 13 = 2 \times 4 \times 2 - (\frac{x v B}{2 x + 9}) 2 x 3 = \frac{16 x^{2}}{2 x + 9} 16 x^{2} - 6 x - 27 = 0 x = \frac{3}{2}$

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