Two parallel rails with negligible resistance are 10 cm long. They are connected by a $5.0 Ω$ resistor. The circuit also contains two metal rods having resistance of $10 Ω$ and $15 Ω$ along the rails. The rod are pulled with constant speed 4.00 m/s and 2 m/s. A uniform magnetic field of magnitude 0.01 T is applied perpendicular to the plane of the rails. The current in the $5 Ω$ resistor is $\frac{k}{55} m A .$ Find k.

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answer is 8.

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Detailed Solution

$ε_{1} = B l V_{1} = \frac{1}{250} V$
$ε_{2} = B l V_{2} = \frac{1}{500} V$
$\frac{1}{250} - 10 i - 5 i_{1} = 0$ …(1)
$- 20 i_{1} + 15 i = \frac{1}{500}$ …(2)
$k = 8$

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