We have seen that the heart produces a magnetic field that...

We have seen that the heart produces a magnetic field that can be used to diagnose problems with the heart. The magnetic field of the heart is a dipole field produced by a loop current in the outer layers of the heart. Suppose that the field at the center of the heart is $90 \mathrm{pT}$ (a p $\mathrm{T}$ is $10^{-12} \mathrm{T}$ ) and that the heart has a diameter of approximately $12 \mathrm{cm}$. What current circulates around the heart to produce this field?

Key Concepts

Magnetic Field from a Current Loop

A current loop produces a magnetic field that circulates around the loop, and at its center, the field can be calculated using formulas derived from the Biot–Savart law. This concept is central in electromagnetism as it explains how moving charges (currents) generate magnetic fields, which is fundamental to many applications including the study of biological magnetic fields like that of the heart.

Biot–Savart Law

The Biot–Savart law provides a method to calculate the magnetic field produced at a point in space by a small segment of current. In the case of a current loop, it relates the magnetic field at the center of the loop to the current, the radius of the loop, and the permeability of free space. This law forms the mathematical basis for determining the current necessary to produce a specific magnetic field value.

Magnetic Dipole

A magnetic dipole is a simple model that describes the magnetic properties of a current loop with a distinct north and south pole. In the context of biological systems like the heart, the dipole model is used to approximate the magnetic field resulting from the organized circulation of electrical currents, simplifying the analysis of complex bio-magnetic phenomena.

Unit Conversions in Electromagnetism

Converting units is an essential step in solving electromagnetism problems, as physical quantities may be provided in various scales such as pT (picoTesla) for magnetic field strength or centimeters for dimensions. Accurate conversion of these units to the standard SI units ensures that all calculations involving constants like the permeability of free space are consistent and correct.

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