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

Question #229889

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?


1
Expert's answer
2021-08-27T08:29:14-0400

Given:

V=12VV=12\:\rm V

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

l=1ml=1\:\rm m

r=1cm=0.01  mr=1\:\rm cm=0.01\; m

ρ=1.5106Ωm\rho=1.5*10^{-6}\:\rm\Omega\cdot m


The current through the wire

I=VR=VρlAI=\frac{V}{R}=\frac{V}{\rho\frac{l}{A}}

I=121.51061π0.0012/4=6.28AI=\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=μ0I2πr=4π1076.282π0.01=1.26104TB=\frac{\mu_0 I}{2\pi r}=\frac{4\pi*10^{-7}*6.28}{2\pi*0.01}=1.26*10^{-4}\:\rm T


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