Biomedical Engineering Reference
In-Depth Information
This equation is used to calculate the energy content of any electric field by
dividing space into finite cubes (or elements). Equation (3.43) is applied to find
the energy content of each cube, and then summed to obtain the total energy. One
2
ε
E
can demonstrate that the energy density in a dielectric medium is
w
=
where
E
2
ε
(
=
K
ε
0
) is the
permittivity
of the medium. This energy density consists of two ele-
2
ε
E
ments: the energy density
0
2
held in the electric field, and the energy density
2
(
KE
−
)
2
ε
0
held in the dielectric medium. The density represents the work done on
the constituent molecules of the dielectric in order to polarize them.
EXAMPLE 3.9
Defibrillators are devices that deliver electrical shocks to the heart in order to convert rapid
irregular rhythms of the upper and lower heart chambers to normal rhythm. In order to
rapidly deliver electrical shocks to the heart, a defibrillator charges a capacitor by apply-
ing a voltage across it, and then the capacitor discharges through the electrodes attached
to the chest of the patient undergoing ventricular fibrillation. In a defibrillator design, a
64-
μ
F capacitor is charged by bringing the potential difference across the terminals of the
capacitor to 2,500V.
(a) How much energy is stored in the capacitor?
(b) How much charge is then stored on the capacitor? What is the average electrical
current (in amperes) that flows through the patient's body if the entire stored charge is
discharged in 10 ms?
Solution:
(a) Using (3.32), the energy stored in the capacitor
1
(
)(
)
2
W
64
10
−
6
2.5
10
3
200J
=
×
×
=
2
(b) Charge stored is
(
)(
)
6
3
3
QC
64
10
−
2.5
10
400
10
−
C
=ΔΦ= ×
×
=
×
ch
m
Alternatively
Q
ch
can also be calculated using (3.27)
3
Q
400
10
−
C
×
ch
Average electrical current
=
40A
=
=
3
time
10
10
−
s
×
3.4.3 Conservation of Charge
Differences in potential within the brain, heart, and other tissues reflect the segre-
gation of electrical charges at certain locations within 3D conductors as nerves are
excited, causing cell membrane potentials to change. While the potential measured
at some distance from an electrical charge generally decreases with increasing dis-
tance, the situation is more complex within the body. For example, generators of
