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Chapter 6. Electricity
Electric Charge
Electric charge comes in two types, which we choose to call positive charge and
negative charge.
Electric charge can be measured using the law for the forces between charges
(Coulomb’s Law).
The coulomb is actually defined in terms of electric current (the flow of electrons),
which is measured in amperes; when the current in a wire is 1 ampere, the amount of
charge that flows past a given point in the wire in 1 second is 1 coulomb. Thus,
Coulomb’s Law
Coulomb’s Law gives the force of attraction or repulsion between two point charges.
If two point charges q1 and q2 are separated by a distance r then the magnitude of the
force of repulsion or attraction between them is
This is the magnitude of the force which each charge exerts on the other charge
(recall Newton’s 3rd law).
If the charges q1 and q2 are of the same sign (both positive or both negative) then
the force is mutually repulsive and the force on each charge points away from the
other charge. If the charges are of opposite signs (one positive, one negative) then
the force is mutually attractive and the force on each charge points toward the other
one.
The Electric Field
Suppose we have a point charge q0 located at r and a set of external charges conspire
so as to exert a force F on this charge. We can define the electric field at the point r
by:
It follows from Coulomb’s law that the electric field at point r due to a charge q
located at the origin is given by
where ˆr is the unit vector which points in the same direction as r.
Potential Difference or Voltage
The electric field is measured in units of volt per meter (or volt per centimeter).
The product of the electric field and the distance over which the field extends is an
important parameter which is called potential difference or voltage.
The voltage (V ) between two points is a measure of energy transfer as the charge
moves between the two points. Potential difference is measured in volts.
Electric Current
An electric current is produced by a motion of charges.
The magnitude of the current depends on the amount of charge flowing past a given
point in a given period of time. Current is measured in amperes (A).
One ampere is 1 coulomb (C) of charge flowing past a point in 1 second (sec).
Electric Circuits
The amount of current flowing between two points in a material is proportional to the
potential difference between the two points and to the electrical properties of the
material. The electrical properties are usually represented by three parameters:
resistance, capacitance, and inductance. Resistance measures the opposition to current
flow. This parameter depends on the property of the material called resistivity, and it
is analogous to friction in mechanical motion.
Capacitance measures the ability of the material to store electric charges. Inductance
measures the opposition in the material to changes in current flow.
Resistor
The resistor is a circuit component that opposes current flow. Resistance (R) is
measured in units of ohm (Ω). The relation between current (I ) and voltage (V ) is
given by Ohm’s law, which is
V =IR
Capacitor
The capacitor is a circuit element that stores electric charges. In its simplest form it
consists of two conducting plates separated by an insulator (see Fig. (6.4).
Capacitance (C) is measured in farads. The relation between the stored charge (Q),
and the voltage across the capacitor is given by
Q = CV
In a charged capacitor, positive charges are on one side of the plate, and negative
charges are on the other. The amount of energy (E) stored in such a configuration is
given by
Inductor
The inductor is a device that opposes a change in the current flowing through it.
Inductance is measured in units called henry.
Electricity and Magnetism
Electricity and magnetism are related phenomena. A changing electric field always
produces a magnetic field, and a changing magnetic field always produces an electric
field. All electromagnetic phenomena can be traced to this basic interrelationship. A
few of the consequences of this interaction follow:
1.
An electric current always produces a magnetic field at a direction perpendicular
to the current flow.
2. A current is induced in a conductor that moves perpendicular to a magnetic field.
3. An oscillating electric charge emits electromagnetic waves at the frequency of
oscillation. This radiation propagates away from the source at the speed of light.
Radio waves, light, and X-rays are examples of electromagnetic radiation.
The Nervous System
The most remarkable use of electrical phenomena in living organisms is found in
the nervous system of animals.
Specialized cells called neurons form a complex network within the body which
receives, processes, and transmits information from one part of the body to another.
The center of this network is located in the brain, which has the ability to store and
analyze information.
Based on this information, the nervous system controls various parts of the body.
The nervous system is very complex. The human nervous system, for example,
consists of about 1010 interconnected neurons.
It is, therefore, not surprising that, although the nervous system has been studied for
more than a hundred years, its functioning as a whole is still poorly understood.
The Nervous System
It is not known how information is stored and processed by the nervous system; nor
is it known how the neurons grow into patterns specific to their functions.
The messages are electrical pulses transmitted by the neurons.
When a neuron receives an appropriate stimulus, it produces electrical pulses that
are propagated along its cablelike structure.
The pulses are constant in magnitude and duration, independent of the intensity of
the stimulus. The strength of the stimulus is conveyed by the number of pulses
produced.
When the pulses reach the end of the “cable,” they activate other neurons or muscle
cells.
The Neuron
The neurons, which are the basic units of the nervous system, can be divided into
three classes: sensory neurons, motor neurons, and interneurons.
(1) The sensory neurons receive stimuli from sensory organs that monitor the
external and internal environment of the body.
Depending on their specialized functions, the sensory neurons convey messages
about factors such as heat, light, pressure, muscle tension, and odor to higher
centers in the nervous system for processing.
(2) The motor neurons carry messages that control the muscle cells.
These messages are based on information provided by the sensory neurons and by
the central nervous system located in the brain.
(3) The interneurons transmit information between neurons.
The Neuron
Each neuron consists of a cell
body to which are attached input
ends called dendrites and a long
tail called the axon which
propagates the signal away from
the cell (see Fig. 6.1).
The far end of the axon branches
into nerve endings that transmit
the signal across small gaps to
other neurons or muscle cells.
Figure (6.1): A neuron.
A simple sensory - motor neuron circuit
A stimulus from a muscle produces nerve impulses that travel to the spine.
Here the signal is transmitted to a motor neuron, which in turn sends impulses to
control the muscle. Such simple circuits are often associated with reflex actions.
(3)
(1)
(2)
Figure (6.2): A simple neural circuit.
Electrical Potentials in the Axon
In the aqueous environment of the body, salt and various other molecules dissociate
into positive and negative ions.
As a result, body fluids are relatively good conductors of electricity.
Still, these fluids are not nearly as conductive as metals; their resistivity is about 100
million times greater than that of copper, for example.
The inside of the axon is filled with an ionic fluid that is separated from the
surrounding body fluid by a thin membrane (Fig. 6.3).
Figure (6.3): The axon membrane and surroundings.
Electrical Potentials in the Axon
The axon membrane, which is only about 50–100 ˚A thick, is a relatively good but
not perfect electrical insulator.
Therefore, some current can leak through it. The electrical resistivities of the internal
and the external fluids are about the same, but their chemical compositions are
substantially different.
The external fluid is similar to sea water. Its ionic solutes are mostly positive
sodium ions and negative chlorine ions. Inside the axon, the positive ions are mostly
potassium ions, and the negative ions are mostly large negatively charged organic
molecules.
Figure (6.3): The axon membrane and surroundings.
Because there is a large concentration of sodium ions outside the axon and a large
concentration of potassium ions inside the axon, we may ask why the
concentrations are not equalized by diffusion.
In other words, why don’t the sodium ions leak into the axon and the
potassium ions leak out of it?
The answer lies in the properties of the axon membrane. In the resting condition,
when the axon is not conducting an electrical pulse, the axon membrane is highly
permeable to potassium and only slightly permeable to sodium ions.
The membrane is impermeable to the large organic ions. Thus, while sodium ions
cannot easily leak in, potassium ions can certainly leak out of the axon. However,
as the potassium ions leak out of the axon, they leave behind the large negative
ions, which cannot follow them through the membrane.
As a result, a negative potential is produced inside the axon with respect to
the outside.
This negative potential, which has been measured to be about 70mV, holds back
the outflow of potassium so that in equilibrium the concentration of ions is as we
have stated.
Some sodium ions do in fact leak into the axon, but they are continuously removed
by a metabolic mechanism called the sodium pump.
This pumping process, which is not yet fully understood, transports sodium ions
out of the cell and brings in an equal number of potassium ions.
Propagation of the Action Potential
After many years of research the
propagation of an impulse along the axon is
now reasonably well understood. (See Fig.
(6.8.)
When the magnitude of the voltage across a
portion of the membrane is reduced below a
threshold value, the permeability of the axon
membrane to sodium ions increases rapidly.
As a result, sodium ions rush into the axon,
cancel out the local negative charges, and, in
fact, drive the potential inside the axon to a
positive value.
This process produces the initial sharp rise
of the action potential pulse.
Figure (6.8): The action potential. (a) The
action potential begins with the axon
membrane becoming highly permeable to
sodium ions (closed circles) which enter the
axon making it positive. (b) The sodium gates
then close and potassium ions (open circles)
leave the axon making the interior negative
again.
Propagation of the Action Potential
The sharp positive spike in one portion of
the axon increases the permeability to the
sodium immediately ahead of it which in
turn produces a spike in that region.
In this way the disturbance is sequentially
propagated down the axon, much as a flame
is propagated down a fuse.
Figure (6.8): The action potential. (a) The
action potential begins with the axon
membrane becoming highly permeable to
sodium ions (closed circles) which enter the
axon making it positive. (b) The sodium gates
then close and potassium ions (open circles)
leave the axon making the interior negative
again.
6.1.7 Synaptic Transmission
Now we shall briefly describe how the pulse is transmitted from the axon to
other neurons or muscle cells.
Through these nerve endings the axon transmits
signals, usually to a number of cells.
In some cases the action potential is transmitted
from the nerve endings to the cells by electrical
conduction.
In the vertebrate nervous system, however, the
signal is usually transmitted by a chemical
substance.
The nerve endings are actually not in contact
with the cells. There is a gap, about a
nanometer wide (1 nm= 10−9 m= 10−7 cm)
between the nerve ending and the cell body.
Figure (6.10): Synapse.
Synaptic Transmission
Now we shall briefly describe how the pulse is transmitted from the axon to
other neurons or muscle cells.
These regions of interaction between the nerve
ending and the target cell are called synapses
(see Fig. 6.10).
When the impulse reaches the synapse, a
chemical substance is released at the nerve
ending which quickly diffuses across the gap
and stimulates the adjacent cell.
Figure (6.10): Synapse.
Often a number of synapses must be activated
simultaneously to start the action potential in
the target cell. The action potential produced by
a neuron is always of the same magnitude.
Electricity in Plants
The type of propagating electrical impulses we have discussed in connection with
neurons and muscle fibers have also been found in certain plant cells.
The shape of the action potential is the same in both cases, but the duration of the
action potential in plant cells is a thousand times longer, lasting about 10 sec.
The speed of propagation of these plant action potentials is also rather slow, only a
few centimeters per second.
In plant cells, as in neurons, the action potential is elicited by various types of
electrical, chemical, or mechanical stimulation. However, the initial rise in the plant
cell potential is produced by an inflow of calcium ions rather than sodium ions.
It is possible that they coordinate the growth and the metabolic processes of the
plant and perhaps control the long-term movements exhibited by some plants.
With my best wishes
Dr. Mohamed Rashad
[email protected]