Rail guns have been suggested for launching projectiles into space without chemical rockets, and for ground-to-air antimissile weapons of war. A tabletop model rail gun (Fig. P30.61) consists of two long parallel horizontal rails 3.50 cm apart, bridged by a bar BD of mass 3.00 g. The bar is originally at rest at the midpoint of the rails and is free to slide without friction. When the switch is closed, electric current is quickly established in the circuit ABCDEA. The rails and bar have low electric resistance, and the current is limited to a constant 24.0 A by the power supply.
(a) Find the magnitude of the magnetic field 1.75 cm from a single very long straight wire carrying current 24.0 A.
(b) Find the magnitude and direction of the magnetic field at point C in the diagram, the midpoint of the bar, immediately after the switch is closed. Suggestion: Consider what conclusions you can draw from the Biot€“Savart law.
(c) At other points along the bar BD, the field is in the same direction as at point C, but larger in magnitude. Assume that the average effective magnetic field along BD is five times larger than the field at C. With this assumption, find the magnitude and direction of the force on the bar.
(d) Find the acceleration of the bar when it is in motion.
(e) Does the bar move with constant acceleration?
(f) Find the velocity of the bar after it has traveled 130 cm to the end of the rails.

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