Magnetoencephalography (MEG) is a technique for measuring changes in the magneti

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 2.70 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 center of the brain.) answer in in A and T thank you very much.

Explanation / Answer

We are approximating the situation with a circular current carrying wire inside each hemisphere of brain

The magnetic field at the centre of a circular current carrying loop is given by Bo = oI/2r   

The magnetic field at a point on the axis of the loop at a distance x from the centre is

B = oIR2 / 2 (x2 + R2 )3/2

R = 65 / 2 = 32.5 mm = 0.0325 m

x = 2.7 cm = 0.027 m

4.75 * 10-15 = 4 × 107 *I* 0.03252 / 2 ( 0.0272 + 0.03252)3/2

4.75 * 10-15 = 8.798285038 x 10-6 * I

I = 5.398779398 x 10-10 A ~ 5.4 x 10-10 A

At the center of hemisphere, Bo = oI/2R

Bo = 4 × 107 * 5.398779398 x 10-10 / (2 *0.0325) = 1.043739427 x 10-14  T

Bo ~ 10.4 x 10-15 T

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