Answer to Question #237202 in Electricity and Magnetism for Lazarus Brown

Question

You have a 12 V battery connected to a single straight nichrome wire in your heater. if the wire is a millimeter thick and a meter long and you place a devise that measures magnetic stregth at a one centimeter distance away from the wire, what will be the reading on this devise?

Answer 1

Nichrome wire has resistivity

$ρ = 1 \times 10^{-6} \; ohm \cdot m \\ l = 1 \;m \\ A = \pi (\frac{d}{2})^2 \\ A = \pi (\frac{1 \times 10^{-3}}{2})^2 \\ A = 7.85 \times 10^{-7} \;m^2$

Resistance of this wire will be

$R = \frac{ρl}{A} \\ R= \frac{1 \times 10^{-6} \times 1}{7.85 \times 10^{-7}} \\ R = 1.27 \; ohm$

Current I in this qire will be

$I = \frac{V}{ R} \\ I = \frac{12}{1.27} \\ I = 9.44 \;A$

Magnetic field at distance R from a wire is given by

$B = \frac{\mu_0 I}{2 \pi R} \\ B = \frac{4 \pi \times 10^{-7} \times 9.44}{2 \pi \times 1. \times 10^{-2} } \\ B = 1.88 \times 10^{-4} \;T$