A bar is sliding along a set of connected conducting rails as shown in Figure P29.37. The bar is given an initial velocity \(\vec{v}_{\mathrm{i}}\) to the right and then allowed to move freely. The bar has mass \(m\), and the distance between the rails (which is also the bar length) is \(\ell\). The resistance of the conducting loop comprising the bar and conducting rails is \(R\). Show that the speed of the bar decreases exponentially with time, and determine the time constant.

Data from Figure P29.37

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