#### Question

The magnetic field 40.0 cm away from a long, straight wire carrying current 2.00 A is 1.00 $\mu \mathrm { T }$. At what distance is it 0.100 $\mu \mathrm { T }$?

#### Solutions

Verified#### Step 1

1 of 5In this problem, we are given that a current-carrying wire has current $I = 2.00~\mathrm{A}$. At a distance $r_{1} = 40.0~\mathrm{cm} = 0.400~\mathrm{m}$, the magnetic field is $B_{1} = 1.00~\mathrm{\mu T}$. We calculate the distance such that the magnetic field is $B_{2} = 0.100~\mathrm{\mu T}$.

#### Step 1

1 of 3$\textbf{Given}$

The current in the wire:

$I= 2 \ A$

The magnetic field:

$B= 0.1 \ \mu T = 1 \cdot 10^{-7} \ T$

$\textbf{Solution}$

a) We are going to start from the Ampere's Law:

$\sum B \Delta l= \mu_0 I$

where $B$ is the magnetic field, $\Delta l$ is the length of the segment which is closed and where we have the magnetic field $B$. $\mu_0$ is the magnetic permeability of the vacuum ($\mu_0=4 \pi \cdot 10^{-7} \ H/m$), and $I$ is the current through the wire, which is creating the magnetic field $B$.