Two long parallel wires are $0.400 \mathrm {~m}$ apart and carry currents of $4.00 \mathrm {~A}$ and $6.00 \mathrm {~A}$. What is the magnitude of the force per unit length that each wire exerts on the other wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \right.$. $\mathrm { m } / \mathrm { A }$ )
A) $12.0 \mu \mathrm { N } / \mathrm { m }$
B) $16.0 \mu \mathrm { N } / \mathrm { m }$
C) $2.00 \mu \mathrm { N } / \mathrm { m }$
D) $38.0 \mu \mathrm { N } / \mathrm { m }$
E) $5.00 \mu \mathrm { N } / \mathrm { m }$

Question

Quizplus · Accepted Answer

The magnitude of the force per unit length that each wire exerts on the other wire is given by:$$F = \frac{\mu_0 I_1 I_2}{2\pi d}$$where:* $\mu_0$ is the permeability of free space* $I_1$ and $I_2$ are the currents in the wires* $d$ is the distance between the wiresPlugging in the given values, we get:$$F = \frac{(4\pi \times 10^{-7} \mathrm{T} \cdot \mathrm{m}/\mathrm{A})(4.00 \mathrm{A})(6.00 \mathrm{A})}{2\pi (0.400 \mathrm{m})}$$$$F = 12.0 \mu \mathrm{N} / \mathrm{m}$$

Two Long Parallel Wires Are 0.400 m0.400 \mathrm {~m}0.400 m Apart and Carry Currents Of

Two Long Parallel Wires Are $0.400 \mathrm {~m}$ Apart and Carry Currents Of