Question

Magnetoencephalography (MEG) is a noninvasive method for studying electrical activity in the brain. It is based on the principle that an electric current creates a magnetic field, whether the current is in a wire or in the neurons of a brain. Thus, your very thoughts at this moment are generating measurable magnetic fields outside your head. With today's technology, an MEG can detect magnetic fields as small as 1.28E-15 T. Approximating a neuron by a straight wire, what electric current is needed to produce this magnetic field strength at a distance of 6.42 cm?

Answer 1

I = 4.11 10⁻¹² A

Step-by-step explanation:

For this exercise we can use Ampère's law, which relates the magnetic flux to the current inside the surface and the magnetic permeability

∫ B. ds = μ₀ I

Let's write a surface that is a circle around the neuron, in this case the direction of the field and the displacement vector are parallel, which reduces the scalar product to an ordinary product

∫B ds = μ₀ I

The field is constant so we take it from the integral that is immediate

B ∫ ds = μ₀ I

B 2π r = μ₀ I

I = B 2π r / μ₀

I = 1.28 10⁻¹⁵ 2π 0.0642 / 4π 10⁻⁷

I = 4.11 10⁻¹² A