# Oscillating pen

A loop is formed of two parallel conductors connected by solenoid of inducation $$L$$ and a conducting pen of mass $$m$$ which can slide freely(without friction) over the conductors. There is a uniform homogeneous magnetic field of induction $$B$$ perpendicular to the plane of loop(horizontal plane). The distance of conductors is $$l$$ . At the moment $$t=0$$ the pen is imparted an initial velocity $$v_0$$ directed to the right. Find the law of motion $$x(t)$$ if the electric resistance is negligible.

$$v_0=1 \textrm{ m/s}$$, $$l=15 \textrm{ cm}$$, $$m=1 \textrm{ g}$$, $$L=4 \textrm{ mH}$$, $$B=0.003 \textrm{ T}$$

Give your answer as $$\frac{x(367)}{10}$$ in meters.

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