Two parallel wires of length 14 m are separated by a distance of a = 0.120 m. Th

Question

Two parallel wires of length 14 m are separated by a distance of a = 0.120 m. The first carries a current of 11 = 1 A and the second a current of 12 1 A in the same direction. Find the force per unit length that wire 2 exerts on wire 1. Conceptualize The current in wire 2 produces a magnetic field that exerts a force on the moving charge in wire 1. Similarly, the current in wire 1 produces a force on wire 2. The two forces are equal in magnitude and opposite in direction Categorize We use the results for the magnetic force between two parallel conductors, based on the Biot-Savart law Analyze The force between the two wires, per unit length, is seen to be 2na Substitute in numerical values (2T)0.120 m Since the currents in the two wires are in the same direction, the force is attractive Finalize How does the force change if the wires are closer together, or if the direction of the current is changed in one of the two wires? How can that be understood in the terms of the magnetic field that the first wire produces at the location of the second wire?

Explanation / Answer

F/l = uoI1I2 / 2pir

= 4pi*10^-7*1*1 / 2pi*0.12

= 1.67*10^-6 N/m

so the force per unit length is 1.67*10^-6 N/m

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