Question #43211

A stationary point object is placed on the principal axis of a convex lens of focal length $f = 20 \text{ cm}$. The lens moves towards the object with an unknown, time-varying velocity. A detector tracks the real image formed by the lens. The detector is mounted on a conducting rod of length $l = 0.5 \text{ m}$ that slides without friction on two parallel conducting rails. The rails are rigidly attached to the lens, parallel to its principal axis, and an ideal inductor of inductance $L = 10 \text{ mH}$ is connected at the lens-end of the rails, forming a closed circuit of negligible resistance. A uniform magnetic field $B = 2.0 \text{ T}$ exists perpendicular to the plane of the rails. At $t=0$, the distance between the object and the first principal focus of the lens is $x_1 = 50 \text{ cm}$, and the current in the inductor is zero. Find the total magnetic energy stored in the inductor at the instant the distance between the object and the first principal focus becomes $x_2 = 10 \text{ cm}$.