For an electric dipole at origin, find the value of ‘tanδ’ at point A (3, 4). Here ‘δ’ is the angle made by resulting electric field at point A with +ve x-axis.
Answers
Explanation:
The first two theoretical methods of this chapter (solid angle theorem and Miller-Geselowitz model) are used to evaluate the electric field in a volume conductor produced by the source - that is, to solve the forward problem. After this discussion is a presentation of methods used to evaluate the source of the electric field from measurements made outside the source, inside or on the surface of the volume conductor - that is, to solve the inverse problem. These methods are important in designing electrode configurations that optimize the capacity to obtain the desired information.
In fact, application of each of the following methods usually results in a particular ECG-lead system. These lead systems are not discussed here in detail because the purpose of this chapter is to show that these methods of analysis form an independent theory of bioelectricity that is not limited to particular ECG applications.
The biomagnetic fields resulting from the electric activity of volume sources are discussed in detail in Chapter 12.
11.2 SOLID ANGLE THEOREM
11.2.1 Inhomogeneous Double Layer
PRECONDITIONS:
SOURCE: Inhomogeneous double layer
CONDUCTOR: Infinite, homogeneous, (finite, inhomogeneous)
The solid angle theorem was developed by the German physicist Hermann von Helmholtz in the middle of the nineteenth century. In this theory, a double layer is used as the source. Although this topic was introduced in Chapter 8, we now examine the structure of a double layer in somewhat greater detail.
Suppose that a point current source and a current sink (i.e., a negative source) of the same magnitude are located close to each other. If their strength is i and the distance between them is d, they form a dipole moment id as discussed in Section 8.2.2. Consider now a smooth surface of arbitrary shape lying within a volume conductor. We can uniformly distribute many such dipoles over its surface, with each dipole placed normal to the surface. In addition, we choose the dipole density to be a well-behaved function of position - that is, we assume that the number of dipoles in a small area is great enough so that the density of dipoles can be well approximated with a continuous function.