A U-shaped conducting wire of mass $$m=10\,\text{g}$$, having length of its horizontal section as $$20\,\text{cm}$$, is free to move vertically up and down. The two ends of the wire are immersed in mercury for proper electrical contact. The wire is in a homogeneous field of magnetic induction $$B=0.1\,\text{T}$$ as shown. The wire jumps up to a height $$h=3\,\text{m}$$ when a charge $$q$$, in the form of a current pulse, is sent through the wire. Considering that the duration of the current pulse is very small compared to the time of flight, the charge $$q$$ passed through the wire is estimated to be nearly