Question

Magnetoencephalography (MEG) is a technique for measuring changes in the magnetic field of the brain caused by external stimuli such as touching the body or viewing images of food. Such a change in the field occurs due to electrical activity (current) in the brain. During the process, magnetic sensors are placed on the skin to measure the magnetic field at that location. Typical field strengths are a few femtoteslas (1 femtotesla = 1 fT = 10�15 T). An adult brain is about 140 mm wide, divided into two sections (called \"hemispheres\" although the brain is not truly spherical) each about 70 mm wide. We can model the current in one hemisphere as a circular loop, 65.0 mm in diameter, just inside the brain. The sensor is placed so that it is along the axis of the loop 2.90 cm from the center. A reasonable magnetic field is 4.75 fT at the sensor. According to this model, what is the current in this hemisphere of the brain?

What is the magnetic field at the center of the hemisphere of the brain?

Answer 1

If we model the system explained in the brain as a circular loop we can apply the next formula for induction magnetic in the center of a curved almost closed of radius r by which flows a current I, which is the following:

B = ₀   I / 2 r   where B, r are magnetic field and radius given fro data problem, ₀ is the permeability of the medium commonly used: ₀ = 4 x 10 ^ -7 T m/ A

Clearing out the current we have:

I = 2 B r / ₀ Sustittuting values and taking r = radius = 2.90 cm = 0.029 m:

I = 2 ( 4.75 x 10 ^-15 T ) ( 0.029 m) / 4 x 10 ^ -7 T m/ A = 1.3775 X 10 ^-16 /1.25663 X 10 -6 = 1.09617 X 10 ^-10 A which is the requested outcome.

b) At the center of the hemisphere of the brain the radius value is 0 so the total current I = 0 A