handbook of modern sensors

3.1 Electric Charges, Fields, and Potentials 43
it becomes subjected to a rotation force (Fig. 3.3B). Usually, a dipole is a part of a
crystal which defines its initial orientation. An electric field, if strong enough, will
align the dipole along its lines. Torque, which acts on a dipole in a vector form, is
τ = pE. (3.12)
Work must be done by an external agent to change the orientation of an electric dipole
in an external electric field. This work is stored as potential energy U in the system
consisting of the dipole and the arrangement used to set up the external field. In a
vector form this potential energy is
U =−pE. (3.13)
A process of dipole orientation is called poling. The aligning electric field must be
strong enough to overcome a retaining force in the crystalline stricture of the material.
To ease this process, the material during the poling is heated to increase the
mobility of its molecular structure. The poling is used in fabrication of piezoelectric
and pyroelectric crystals.
The electric field around the charged object can be described not only by the
vector E, but by a scalar quantity, the electric potential V as well. Both quantities
are intimately related and usually it is a matter of convenience which one to use in
practice.Apotential is rarely used as a description of an electric field in a specific point
of space. A potential difference (voltage) between two points is the most common
quantity in electrical engineering practice. To find the voltage between two arbitrary
points, we may use the same technique as above—a small positive test charge q 0 .If
the electric charge is positioned in point A, it stays in equilibrium, being under the
influence of force q 0 E. Theoretically, it may remain there infinitely long. Now, if we
try to move it to another point B, we have to work against the electric field. Work
(W AB ) which is done against the field (that is why it has negative sign) to move the
charge from A to B defines the voltage between these two points:
V B − V A =− W AB
q 0
. (3.14)
Correspondingly, the electrical potential at point B is smaller than at point A. The SI
unit for voltage is 1 volt = 1 joule/coulomb. For convenience, point A is chosen to be
very far away from all charges (theoretically at an infinite distance) and the electric
potential at that point is considered to be zero. This allows us to define the electric
potential at any other point as
V =− W . (3.15)
q 0
This equation tells us that the potential near the positive charge is positive, because
moving the positive test charge from infinity to the point in a field, must be made
against a repelling force. This will cancel the negative sign in formula (3.15). It should
be noted that the potential difference between two points is independent of the path
along which the test charge is moving. It is strictly a description of the electric field