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 place a device that measures magnetic field strength at a one-centimeter distance away from the wire, what will be the reading on this device?

Answer 1

Device is placed very near the wire then wire will behave as a infinite long current carrying wire.

Magnetic field strength due to current carrying wire is given by

$B = \mu_0 \times \frac{i}{2 \pi d} \\ \mu_0= 4 \pi \times 10^{-7} \\$

d = distance of device from wire = 1 cm = 0.01 m

i = current in wire $= \frac{E}{R}$ (from ohm's law)

E = apply battery voltage = 12 V

R = resistance of wire $= \rho \times \frac{L}{A}$

$\rho$ = resistivity of Nichrome = $1.0 \times 10^{-6} \; ohm \times m$

L = Length of wire = 1 m

A = cross sectional area of wire $= \frac{\pi d^{2}}{4}$

d = diameter of wire = thickness of wire = 1 mm = 0.001 m

$i = \frac{12}{\frac{(1.0 \times 10^{-6}) \times 1}{(0.25 \times \pi \times 0.001^2)}} = 9.425 \; A \\ B = \frac{(4 \times \pi \times 10^{-7}) \times 9.425}{(2 \pi \times 0.01)} \\ B = 0.0001885 \; T \\ B = 1.885 \times 10^{-4} \; T$