Скачать или смотреть The Boundary Conditions at a Conductor / Free Space Interface

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When there is no charge in the interior of a conductor (p = 0), E must be zero be- cause, according to Gauss's law, the total outward electric flux through any closed surface constructed inside the conductor must vanish.

The charge distribution on the surface of a conductor depends on the shape of the surface. Obviously, the charges would not be in a state of equilibrium if there were a tangential component of the electric field intensity that produces a tangential force and moves the charges. Therefore, under static conditions the E field on a conductor surface is everywhere normal to the surface. In other words, the surface of a conductor is an equipotential surface under static conditions. As a matter of fact, since E = 0 everywhere inside a conductor, the whole conductor has the same elec- trostatic potential. A finite time is required for the charges to redistribute on a con- ductor surface and reach the equilibrium state. This time depends on the conductivity of the material. For a good conductor such as copper this time is of the order of 10-19 (s), a very brief transient. (This point will be elaborated in Section 5-4.)

Figure 3-18 shows an interface between a conductor and free space. Consider the contour abcda, which has width abcd = Aw and height be da = Ah. Sides ab and cd are parallel to the interface. Applying Eq. (3-8), letting Ah 0, and noting that E in a conductor is zero, we obtain immediately Jabeda Edl= Ε, Δw = 0 E, = 0, or (3-71)

which says that the tangential component of the E field on a conductor surface is zero
Hence, the normal component of the E field at a conductor free space boundary is equal to the surface charge density on the conductor divided by the permittivity of free space. Summarizing the boundary conditions at the conductor surface, we have

103

Boundary Conditions at a Conductor/Free Space Interface

E, = 0

(3-71)

In Ps

(3-72)

When an uncharged conductor is placed in a static electric field, the external field will cause loosely held electrons inside the conductor to move in a direction opposite to that of the field and cause net positive charges to move in the direction of the field. These induced free charges will distribute on the conductor surface and create an induced field in such a way that they cancel the external field both inside the conductor and tangent to its surface. When the surface charge distribution reaches an equilibrium, all four relations, Eqs. (3-69) through (3-72), will hold; and the conductor is again an equipotential body
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