Question

A conducting bar with mass m and length $L$ slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current $I$ in the rails and bar, and a constant, uniform, vertical magnetic field $\overrightarrow{B}$ fills the region between the rails ($\textbf{Fig. P27.65}$). (a) Find the magnitude and direction of the net force on the conducting bar. Ignore friction, air resistance, and electrical resistance. (b) If the bar has mass $m$, find the distance $d$ that the bar must move along the rails from rest to attain speed $v$. (c) It has been suggested that rail guns based on this principle could accelerate payloads into earth orbit or beyond. Find the distance the bar must travel along the rails if it is to reach the escape speed for the earth (11.2 km/s). Let $B =$ 0.80 T, $I =$ 2.0 $\times$ 10$^3$ A, $m =$ 25 kg, and $L =$ 50 cm. For simplicity assume the net force on the object is equal to the magnetic force, as in parts (a) and (b), even though gravity plays an important role in an actual launch in space.

          A conducting bar with mass m and length $L$ slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current $I$ in the rails and bar, and a constant, uniform, vertical magnetic field $\overrightarrow{B}$ fills the region between the rails ($\textbf{Fig. P27.65}$). (a) Find the magnitude and direction of the net force on the conducting bar. Ignore friction, air resistance, and electrical resistance. (b) If the bar has mass $m$, find the distance  $d$ that the bar must move along the rails from rest to attain speed $v$. (c) It has been suggested that rail guns based on this principle could accelerate payloads into earth orbit or beyond. Find the distance the bar must travel along the rails if it is to reach the escape speed for the earth (11.2 km/s). Let $B =$ 0.80 T, $I =$ 2.0 $\times$ 10$^3$ A, $m =$ 25 kg, and $L =$ 50 cm. For simplicity assume the net force on the object is equal to the magnetic force, as in parts (a) and (b), even though gravity plays an important role in an actual launch in space.

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