Chapter 20, Problem 82PP

BIO The human heart consists largely of elongated muscle cells, some 100μm long and 15 μm in diameter. In its resting state, a cell contains two concentric layers of charge, which confine the electric field to the cell membrane (Fig. 20.38a). When the heart contracts, a wave of depolarization sweeps through, depicting charge and giving each cell a dipole moment (Fig. 20.38b). As a result, the entire organ acts like an electric dipole, producing an external field, which is indirectly detected by electrocardiography. Although the direction of the heart’s dipole moment varies. Fig. 20.38c is typical. In answering the questions that follow, consider the heart in isolation—don’t concern yourself with the effect of surrounding tissues on its electric field.

FIGURE 20.38 Heart cells (a) in the resting state and (b) partially depolarized, resulting in a dipole moment $\stackrel{\to }{p}$. (c) Typical orientation of the heart's dipole moment vector. Cells along the line are depolarizing.

At a distance r, far from the heart, the heart’s electric field

1. a. falls off as 1/r.
2. b. falls off as 1/r².
3. c. falls off as 1/r³.
4. d. falls off as 1/r⁴.