Page 41 - Maxwell House

BASIC EQUATIONS OF MACROSCOPIC ELECTRODYNAMICS 21

space, we can connect two separated points by an infinite number of different ways of different
length and produce, at first glance, different amount of work. It is true, except the case of
electrostatic, i.e. independent of time electric fields.
We will come back to this topic later. Note in
conclusion// that a unit of energy commonly used in
physics is the electron-volt [eV] defined as the
energy gained or lost by single electron or proton
when it moves through a potential difference of 1
Volt, 1 [eV] = 1.60 ∙ 10 −19 [J].

Figure 1.6.2 Line of force, electric 1.6.3 Line of Force
vector direction and strength Equation (1.21) tells us that the monopole sensor
continuously borrows the maximum energy from a
given electric field and faster increases its kinetic energy if the scalar product ∘ = ∙ .
In other words, the electric field vector must be tangential to the contour L at any point of L.
One of this kind contour L, shown in Figure 1.6.2, is called the imaginary line of force if

1. The magnitude of electric field is constant ( = const.) along the contour L.
2. The tangent at any point to it gives the direction of the E-field vector or at the point

P or .
3. E-field lines begin at positive charges and end at negative charges (see Figure 1.6.3). The
number of lines beginning or ending on any particular charge is proportional to the charge
value.

Note some additional evident properties of lines of force (Figure 1.6.2):

1. Two lines never intersect or touch. Think why.
2. At every position, the magnitude of the E-field is proportional to the field line density, i.e.
they are closer (congested) where E-field is stronger and the lines spread out where the E-
field is weaker. Thus, the relative closeness of the lines in some area is the evidence of the
higher intensity of fields, i.e. | | >

| |.

3. In a uniform field, the lines of
force are straight parallel and
uniformly spaced.
a) b)
Figure 1.6.3 illustrates the lines of
5
Figure 1.6.3 Lines of E-force around a) point-like force nearby the point-like charges.
charges, b) dipole The perfectly straight green arrows
in Figure 1.6.3a demonstrate the
structure of the electric fields from the single positive charge or monopole, while the yellow
arrows in Figure 1.6.3b show the same but for the dipole shown in Figure 1.4.1. The higher
density of arrows close to the charge corresponds to higher electric field strength there. By
definition, the force lines start on positive charges and all finish on infinity if the charge is alone
(Figure 1.6.3a) and partially on the negative charge (Figure 1.6.3b) in the case of the dipole.
Eventually, the line of force density is maximum nearby the charges. Unfortunately, though

5 Public Domain Image, source: a2physicsmontessori.weebly.com/review-electricity-and-
magnetism.html, web.ncf.ca/ch865/graphics/EFldPosChargedSphere.jpeg