handbook of modern sensors

3.1 Electric Charges, Fields, and Potentials 39
(A)
(B)
Fig. 3.1. (A) Positive test charge in the vicinity of a charged object and (B) the electric field of
a spherical object.
perfect isolator, the isolating ability of fused quartz is about 10 25 times as great as
that of copper, so that for practical purposes, many materials are considered perfect
isolators. The semiconductors are intermediate between conductors and isolators in
their ability to conduct electricity. Among the elements, silicon and germanium are
well-known examples. In semiconductors, the electrical conductivity may be greatly
increased by adding small amounts of other elements; traces of arsenic or boron are
often added to silicon for this purpose.
Figure 3.1A shows an object which carries a positive electric charge q. If a small
positive electric test charge q 0 is positioned in the vicinity of a charged object, it will
be subjected to a repelling electric force. If we place a negative charge on the object, it
will attract the test charge. In vector form, the repelling (or attracting) force is shown
as f. The boldface indicates a vector notation. A fact that the test charge is subjected
to force without a physical contact between charges means that the volume of space
occupied by the test charge may be characterized by a so-called electric field.
The electric field in each point is defined through the force as
E = f q 0
. (3.1)
Here, E is vector in the same direction as f because q 0 is scalar. Formula (3.1) expresses
an electric field as a force divided by a property of a test charge. The test charge must
be very small not to disturb the electric field. Ideally, it should be infinitely small;
however, because the charge is quantized, we cannot contemplate a free test charge
whose magnitude is smaller than the electronic charge: e = 1.602 × 10 −19 C.
The field is indicated in Fig. 3.1A by the field lines which in every point of space
are tangent to the vector of force. By definition, the field lines start on the positive
plate and end on the negative. The density of field lines indicates the magnitude of
the electric field E in any particular volume of space.