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

`3.81972* 10^(-7)\ A`

Step-by-step explanation:

B = Magnetic field =
`3* 10^(-8)\ G`

d = Diameter of loop = 16 cm

r = Radius =
`(d)/(2)=(16)/(2)=8\ cm`

i = Current

`\mu_0` = Vacuum permeability =
`4\pi * 10^(-7)\ H/m`

The magnetic field of a loop is given by

`B=(\mu_0i)/(2r)\\\Rightarrow i=(B2r)/(\mu_0)\\\Rightarrow i=(3* 10^(-8)* 10^(-4)* 2* 0.08)/(4\pi* 10^(-7))\\\Rightarrow i=3.81972* 10^(-7)\ A`

The current needed to produce such a field at the center of the loop is
`3.81972* 10^(-7)\ A`