Rail guns have been suggest for launching projectiles into space without chemica

Question

Rail guns have been suggest for launching projectiles into space without chemical rockets and for ground-to-air antimissile weapons. A tabletop model rail gun consists of two long, parallel, horizontal rails 0.035 m apart, bridged by a bar BD of a mass of .003 kg. The bar is originally 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 constance 24.0 A by the power supply. Find the magnitude of the magnetic field 1.75 cm from a single very, long straight wire carrying current 24.0 A. Find the magnitude and direction of the magnetic field at a point C in the diagram, the midpoint of the bar, immediately after the switch is closed.

Explanation / Answer

Using Ampere's Law: B · dl = 0 (I) ; where I is the current, and dl is the circumference of a concentric circle around the wire, with a radius of 1.75cm, or .0175 m.

So: B [2(.0175)] = 24 *0

B = 218.27 * 0 (I don't know 0 off the top of my head, it's a constant though.)

Using the right hand rule, and opposite currents from either wire, we find that the B field is directed down (perpendicular to the plane of the circuit) and is double the B field induced from each wire. The distance from C to either wire is .0175, and we already calculated the B field from each wire at that distance. Double the previous answer to get 436.54 0 (and the units would be Teslas) :)

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