Question

The body contains many small currents caused by the motion of ions in the organs and cells. Measurements of the magnetic field around the chest due to currents in the heart give values of about$\mathbf{10}\mathit{\mu }\mathit{G}$ . Although the actual currents are rather complicated, we can gain a rough understanding of their magnitude if we model them as a long, straight wire. If the surface of the chest is 5 cm from this current, how large is the current in the heart?

Short answer

The magnitude of the current is$2.5\times {10}^{-4}A$ .

Step-by-step solution

Formula of magnetic field

Treat the wire as a very long wire in this case.

Magnetic field due to a very long wire is given by$\mathit{B}\mathbf{=}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{I}}{\mathbf{2}\mathbf{\pi r}}$ .

Calculate the current

Given that$B=10\mu G$ and$r=5cm$ . The current is given by

$\begin{array}{r}I=\frac{2\pi rB}{{\mu }_0}\\ I=\frac{2\pi \times 0.05\times {10}^{-9}}{4\pi \times {10}^{-7}}\\ I=2.5\times {10}^{-4}\mathrm{A}\end{array}$

So, the magnitude of the current is$2.5\times {10}^{-4}A$ .