Page 129 - Electromagnetics

Figure 3.2: Positive point charge near a grounded conductor.

higher the conductivity, the farther an electron may move on average before undergoing
a collision.
Let us examine how a state of equilibrium is established in a conductor. We shall con-
sider several important situations. First, suppose we bring a positively charged particle
into the vicinity of a neutral, insulated conductor (we say that a conductor is “insulated”
if no means exists for depositing excess charge onto the conductor). The Lorentz force
on the free electrons in the conductor results in their motion toward the particle (Figure
3.1). A reaction force F attracts the particle to the conductor. If the particle and the
conductor are both held rigidly in space by an external mechanical force, the electrons
within the conductor continue to move toward the surface. In a metal, when these elec-
trons reach the surface and try to continue further they experience a rapid reversal in the
direction of the Lorentz force, drawing them back toward the surface. A sufficiently large
force (described by the work function of the metal)will be able to draw these charges
from the surface, but anything less will permit the establishment of a stable equilibrium
at the surface. If σ is large then equilibrium is established quickly, and a nonuniform
static charge distribution appears on the conductor surface. The electric field within the
conductor must settle to zero at equilibrium, since a nonzero field would be associated
with a current J = σE. In addition, the component of the field tangential to the surface
must be zero or the charge would be forced to move along the surface. At equilibrium,
the field within and tangential to a conductor must be zero. Note also that equilibrium
cannot be established without external forces to hold the conductor and particle in place.
Next, suppose we bring a positively charged particle into the vicinity of a grounded
(rather than insulated)conductor as in Figure 3.2. Use of the term “grounded” means
that the conductor is attached via a filamentary conductor to a remote reservoir of charge
known as ground; in practical applications the earth acts as this charge reservoir. Charges
are drawn from or returned to the reservoir, without requiring any work, in response to
the Lorentz force on the charge within the conducting body. As the particle approaches,
negative charge is drawn to the body and then along the surface until a static equilibrium
is re-established. Unlike the insulated body, the grounded conductor in equilibrium has
excess negative charge, the amount of which depends on the proximity of the particle.
Again, both particle and conductor must be held in place by external mechanical forces,
and the total field produced by both the static charge on the conductor and the particle
must be zero at points interior to the conductor.
Finally, consider the process whereby excess charge placed inside a conducting body
redistributes as equilibrium is established. We assume an isotropic, homogeneous con-
ducting body with permittivity and conductivity σ. An initially static charge with

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