Question

The magnetic field around the head has been measured to be approximately 3.00×10−8 gauss . Although the currents that cause this field are quite complicated, we can get a rough estimate of their size by modeling them as a single circular current loop 16.0 cm (the width of a typical head) in diameter.What is the current needed to produce such a field at the center of the loop? Answer in A.

Answer 1

Answer:

$3.81972\times 10^{-7}\ A$

Explanation:

B = Magnetic field = $3\times 10^{-8}\ G$

d = Diameter of loop = 16 cm

r = Radius = $\frac{d}{2}=\frac{16}{2}=8\ cm$

i = Current

$\mu_0$ = Vacuum permeability = $4\pi \times 10^{-7}\ H/m$

The magnetic field of a loop is given by

$B=\frac{\mu_0i}{2r}\\\Rightarrow i=\frac{B2r}{\mu_0}\\\Rightarrow i=\frac{3\times 10^{-8}\times 10^{-4}\times 2\times 0.08}{4\pi\times 10^{-7}}\\\Rightarrow i=3.81972\times 10^{-7}\ A$

The current needed to produce such a field at the center of the loop is $3.81972\times 10^{-7}\ A$