A straight wire carries a 12-A current eastward and a second straight wire carries a 14-A current westward. The wires are separated by a distance of 42 cm. The force per unit length on the wire carrying 12 A is A)8.0 × 10^-5 N/m. B)5.1 × 10^-7 N/m. C)5.1 × 10^-4 N/m. D)5.1 × 10^-6 N/m. E)8.0 × 10^-7 N/m.

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Quizplus · Accepted Answer

The force per unit length on the wire carrying 12 A is given by:$$F = \frac{\mu_0}{4\pi} \frac{2I_1I_2}{d}$$where:$$\mu_0$$ is the permeability of free space ($$4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}$$)$$I_1$$ is the current in the first wire (12 A)$$I_2$$ is the current in the second wire (14 A)$$d$$ is the distance between the wires (42 cm = 0.42 m)Plugging in the values, we get:$$F = \frac{4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}}{4\pi} \frac{2(12 	ext{ A})(14 	ext{ A})}{0.42 	ext{ m}} = 8.0 	imes 10^{-5} 	ext{ N/m}$$Therefore, the correct answer is A.

A Straight Wire Carries a 12-A Current Eastward and a Second