Question

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 5.4 cm from the neuron.

Answer 1

Given Magnetic field is,

$$ \mathrm{B}=1.0^{*} 10^{-15} \mathrm{~T} $$

The distance is,

$$ \begin{aligned} \mathrm{R} &=5.4^{*} 10^{-2} \mathrm{~m} \\ \mu_{0} &=4 \pi^{*} 10^{-7} \mathrm{H} / \mathrm{m} \end{aligned} $$

We have the formula for magnetic field due to a long straight conductor carrying current as

$$ \begin{array}{l} \mathrm{B}=\mu_{0} \mathrm{I} / 2 \pi \mathrm{R} \\ \mathrm{I}=\mathrm{B}(2 \pi \mathrm{R}) / \mu_{0} \end{array} $$

Calculate for I

$$ \begin{aligned} I &=\frac{B(2 \pi R)}{\mu_{0}} \\ &=\frac{\left(1.0 \times 10^{-15} \mathrm{~T}\right)(2 \pi(0.054 \mathrm{~m}))}{4 \pi \times 10^{-7}} \\ &=2.7 \times 10^{-10} \mathrm{~A} \end{aligned} $$

Answer 2

5.4x10m, T r = 5.4cm = Griven, B = 1x10 using the formula, B= po I 2TH I = (275)(B) to Ho Io = (27) (5 4x10²) (x103) = 2.7x10 -7 42 x 10 Anywani - to = 2.7X010 AT A required is 2.7 x to Thus, the wrrent