Two parallel long smooth conducting rails separated by a distance \( \ell=10 \mathrm{~cm} \) are...

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Two parallel long smooth conducting rails separated by a distance \( \ell=10 \mathrm{~cm} \) are connected by a movable conducting connector of mass \( m=4 \mu \mathrm{g} \). Terminals of the rails are connected by the resistor \( R=2 \Omega \) and the capacitor \( C=1 \mu \mathrm{F} \) as shown. A uniform magnetic field \( B=20 \mathrm{~T} \) perpendicular to the plane of the rails is switched on. The connector is dragged by a constant force \( F=10 \mathrm{~N} \). The speed of the connector as function of time if the force \( F \) is applied at \( t=0 \) is equal to \( v=5\left(1-e^{-x \times 10^{4} \times t}\right) \mathrm{m} / \mathrm{s} \). Find the value of \( x \).
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