Question

A very long wire carries an unknown current. At a distance of 30 cm from the wire, the magnitude of the magnetic field is found to be 40 uT. What is the magnitude of the current flowing in the wire?

Answer 1

Given that the distance from the wire is r = 30 cm = 0.3 m

The magnitude of the magnetic field is

$\begin{gathered} \text{B = 40}\mu T \\ =4\times10^{-5}\text{ T} \end{gathered}$

We have to find the magnitude of the current.

The formula to find the magnitude of the current is

$\begin{gathered} B=\text{ (}\frac{\mu_o}{4\pi}\text{)}\times\frac{2I}{r} \\ B\text{ = }\frac{4\pi\times10^{-7}}{4\pi}\times\frac{2I}{r} \\ I=\text{ }\frac{Br}{2}\times10^7\text{ } \end{gathered}$

Substituting the values, the current will be

$\begin{gathered} I\text{ =}\frac{4\times10^{-5}\times0.3}{2}\times10^7 \\ =\text{ 60 A} \end{gathered}$

Thus, the magnitude of current is 60 A