agnetaencephalography (MEG) is a technique for measuring changes in the magnetic

Question

agnetaencephalography (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. Durinçj 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 2.30 cm from the center. A reasonable magnetic field is 6.15 fT at the sensor. According to this model, what is the current in the brain? what is the magnitude field at the center of the hemisphear of the brain?

Explanation / Answer

A)

magnetic field along the axis of the circular loop is given by :

B = (u/4*pi)*(2*pi*R^2*I/(z^2+R^2)^3/2)

where R = radius of the loop = 65/2 mm = 32.5 mm = 0.0325 m

z = distance from the center of the axis = 2.3 cm = 0.023 m

u = permeability of free space = 1.26*10^-6

I = current

B = 4.15 fT = 4.15*10^-15 T

So, magnetic field, B = (1.26*10^-6/(4*3.14))*(2*3.14*0.0325^2*I)/(0.023^2+0.0325^2)^(3/2) = 4.15*10^-15

So, 1.054*10^-5*I = 4.15*10^-15

So, I = 3.94*10^-10 A <--------------answer(A)

B)

At the center of the brain, z = 0

So, B = (u/4*pi)*(2*pi*R^2*I/(R^2)^3/2)

=  (1.26*10^-6/(4*3.14))*(2*3.14*0.0325^2*3.94*10^-10)/(0.0325^2)^(3/2)

= 7.64*10^-15 T <-------------answer

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