JEE Advanced 2019 Paper 2

A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH 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 = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is x×10−3A, where the value of x is _____
[Assume the velocity of wire PQ remains constant (1 cm’s) after key S is closed.
Given:e−1=0.37, where e is base of the natural logarithm]