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only be used if the ﬁeld is constant between the two points, which will often only be true when the points
are very close together. 2.3 Electric Dipole An electric dipole is an object that has no net charge; i.e. a dipole has equal amounts of positive
and negative charge separated from one another. The simplest dipole is two point charges, +q and −q,
separated by a distance d . The electric dipole moment has magnitude p = qd . It is often written as a vector
that points from the negative charge to the positive charge. This direction is called the axis of the dipole.
Though a dipole made of two point charges is a very simplistic model, we can use this to understand
the dipole of the heart. The atria are one end of the dipole and the ventricles are the other end. As the
action potential moves through the heart, the location of positive charge and negative charge exchange
places, making the axis of the heart’s dipole rotate.
The potential from a dipole is fairly straightforward to calculate . Because potential is a scalar, the
potentials from +q and −q add together. Knowing the potential of a single point charge to be
4πε0 r (2) we can use this equation twice to ﬁnd the potential from a dipole.
V = V+ + V− = 1
r+ r− (3) Most dipoles in nature, including those of the heart, are quite small. A reasonable assumption is that
we are interested in measuring the potential very far away from the dipole (r d , where d is the distance 2 between the charges). This lets us approximate that r− − r+ ≈ d cos θ and r− r+ ≈ r2 . Making these
1 p cos θ
where p is the magnitude of the dipole moment and θ is the measured from the axis of the dipole.
V = V+ + V− = 2.4 Electrical Behavior of the Human Heart At rest, the heart muscles are polarized with unequal concentrations of ions across the cell membranes.
There are more positive sodium ions on the outside of the membrane, causing the outside to be slightly
positive relative to the inside. Typically, this resting potential (the potential difference between the inside
and outside of the cell membrane) is about 90 mV. Figure 1(a) shows a section view of a cell membrane.
You will notice that this arrangement looks very, very similar to a parallel plate capacitor, which you will
study in a future lab. Figure 1: (a) A section view of a cell membrane, showing the resting potential from the different concentrations of sodium ions inside compared to outside. (b) Anatomical drawing of a human heart. The red
arrows indicate the direction of travel of the electrical signal.
Cell membranes are typically impermeable to the entry of sodium, but the permeability can be increased if the muscle cell is stimulated. Voltage-gated channels allow the sodium ions to migrate into the
cell, causing a change in the electric ﬁeld surrounding the cell. The change in cell potential from negative to positive (depolarization) and back to negative (repolarization) is a voltage pulse called the action
potential, which, in muscles, causes contraction.
Muscle contraction of the heart occurs spontaneously, causing the heart to act as a pump. In the
upper wall of the right atrium, there is a group of cells known as the sinoatrial (SA) node for which
the spontaneous depolarization is particularly apparent, and this acts as the heart’s pacemaker since the
depolarization of the SA node leads to the succe...
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This document was uploaded on 02/15/2014.
- Spring '14