A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward. The wires are parallel to each other and are 42 cm apart. Calculate the force on a 6.4 m length of one of the wires. (μ0 = 4π × 10^-7 T ∙ m/A)

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Quizplus · Accepted Answer

The force between two parallel wires is given by:$$F = \frac{\mu_0 I_1 I_2 L}{2\pi d}$$where:* F is the force in newtons* μ0 is the permeability of free space (4π × 10^-7 T ∙ m/A)* I1 and I2 are the currents in the wires in amperes* L is the length of the wires in meters* d is the distance between the wires in metersPlugging in the given values, we get:$$F = \frac{(4\pi 	imes 10^{-7} 	ext{ T} \cdot 	ext{m/A})(12 	ext{ A})(14 	ext{ A})(6.4 	ext{ m})}{2\pi (0.42 	ext{ m})}$$$$F = 5.1 	imes 10^{-4} 	ext{ N}$$Therefore, the force on a 6.4 m length of one of the wires is 5.1 × 10^-4 N.

A Very Long Straight Wire Carries a 12-A Current Eastward