A 10cm long perfectly conducting wire PQ is moving, with a velocity...

A $10cm$ long perfectly conducting wire $PQ$ is moving, with a velocity $1cm / s$ on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor $L = 1mH$ and a resistance $R = 1Ω$ as shown in figure. The horizontal rails, $L and R$ lie in the same plane with a uniform magnetic field $B = 1T$ perpendicular to the plane. If the key $S$ is closed at certain instant, the current in the circuit after $1$ milli second is $x \times {10}^{- 3}A,$ where the value of $x$ is_______.
[Assume the velocity of wire $PQ$ remains constant $\left(1cm / s\right)$ after key $S$ is closed. Given: ${e}^{- 1} = 0.37,$ where $e$ is base of the natural logarithm]