At what distance from a long straight wire carrying a current of $5.0 \mathrm {~A}$ is the magnitude of the magnetic field due to the wire equal to the strength of Earth's magnetic field of about $5.0 \times 10 ^ { - 5 } \mathrm {~T}$ ? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

Question

Quizplus · Accepted Answer

The magnetic field $B$ at a distance $r$ from a long straight wire carrying a current $I$ is given by $B = \frac{\mu_0 I}{2\pi r}$. Substituting $B = 5.0 \times 10^{-5} \mathrm{T}$, $I = 5.0 \mathrm{A}$, and $\mu_0 = 4\pi \times 10^{-7} \mathrm{T\cdot m/A}$, and solving for $r$ gives $r = 0.02 \mathrm{m}$ or $2.0 \mathrm{cm}$.

At What Distance from a Long Straight Wire Carrying a Current