Answer to Question #229889 in Electricity and Magnetism for Frieda Kaulinge

Question

You have a 12V battery connected to a single straight nichrome wire in your heater. If the wire is a millimeter thick and a meter long, and you placed a device that measures magnetic field strength at a 1cm distance away from the wire, what will be the reading on this device?

Answer 1

Given:

$V=12\:\rm V$

$d=1\:\rm mm=0.001\: m$

$l=1\:\rm m$

$r=1\:\rm cm=0.01\; m$

$\rho=1.5*10^{-6}\:\rm\Omega\cdot m$

The current through the wire

$$I=\frac{V}{R}=\frac{V}{\rho\frac{l}{A}}$$

$$I=\frac{12}{1.5*10^{-6}*\frac{1}{\pi*0.001^2/4}}=6.28\:\rm A$$

The magnetic field strength at a 1cm distance away from the wire

$$B=\frac{\mu_0 I}{2\pi r}=\frac{4\pi*10^{-7}*6.28}{2\pi*0.01}=1.26*10^{-4}\:\rm T$$