At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the $\vec { B }$ field due to the wire equal to the Earth's $\vec { B }$ field of about 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T ∙ m/A)

Question

Quizplus · Accepted Answer

The magnetic field at a distance r from a long straight wire carrying a current I is given by:
$\vec { B }=\frac { \mu _{0}I }{ 2\pi r }$
We can rearrange this equation to solve for r:
r=$\frac { \mu _{0}I }{ 2\pi B }$
Substituting the given values, we get:
r=$\frac { 4\pi \times10^{-7}\text { T}\cdot\text { m/A}\cdot5.0\text{ A} }{ 2\pi\times5.0\times10^{-5}\text{ T} }=2.0\text{ cm}$
Therefore, the answer is (C) 2.0 cm.

At What Distance from a Long Straight Wire Carrying a Current