   Chapter 19, Problem 45P

Chapter
Section
Textbook Problem

Neurons in our bodies carry weak currents that produce detectable magnetic fields. A technique called magnetoencephalography, or MEG, is used to study electrical activity in the brain using this concept This technique is capable of detecting magnetic fields as weak as 1.0 × 10−15 T. Model the neuron as a long wire carrying a current and find the current it must carry to produce a field of this magnitude at a distance of 4.0 cm from the neuron.

To determine
The current the neuron has to carry to produce the given magnetic field.

Explanation

Given info: The MEG technique can detect magnetic field as weak as 1.0×1015T . The magnetic field has to be measured at 4.0cm from the neuron.

Explanation:

When the neuron is modeled as a long wire carrying current, the magnetic field will be

B=μ0I2πr

• μ0 is the permeability of free space
• I is the current
• r is the distance of the point from the straight conductor

On re-arrangement,

I=2πrBμ0

Substitute 4π×107TmA-1 for μ0 , 1.0×1015T for B , 4.0cm for r to determine the current,

I=2π(4

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