EM11_current in conductor

Introduction
The current is defined as the macro 宏 观 -directional movement of the electric charges under the action of the electric field.
The current remained unchanged with the varying time is
Then:
Ohm's Law in Conductive Media
Ideal 理想Conductor
Conductor with infinite conductivity Obviously, the current can exist in ideal conductor, but the
electric field doesn’t exist in it, for the reason that the field will produce an infinitely large current, which will cause an infinitely large energy, but there is no infinitely large energy.
Inside the power supply, when existing external force, positive charge continuously move to the positive electrode, while negative charge move to the negative electrode, which supply the charge to the electrode, and then maintain the current in the conductor. . The external force can be treated as the external electric field, thus the inner power supply has both internal and external electric field, differential form of the Ohm’s Law inside the power supply can be expressed as: P N
In order to maintain the current, the electric field inside the
conductor should remain unchanged, that is to supplement the outflow electrons, which can be achieved by connect the conductor to a power supply.
Ideal Dielectric (insulator绝缘体)
Dielectric material with a zero value conductivity.
Ohm's Law in Conductive Media
The outer electric field cause the movement of the electrons in conductor, which generate an inner electric field in conductor, which will offset the outer field, the electrons remain static when inner and outer field reach a balance level, and the current is also disappeared.

V V
ˆ J dsdl Il J ndv
l S
l ˆ n
S
J
ˆ US
U voltage
Ohm's Law in Conductive Media
Il US l l U I RI R － Wire Resistance S S This formula is the Ohm’s Law for the circuit theory, called the Integral Form of the Ohm’s Law. It’s seen that the differential form shows the microscopic微观 characteristics of the conductive media, which is applicable to any continuous conductive media, any conduction current and electric field. The integral form shows macroscopic 宏 观 characteristics of the conductive media with finite volume, which is applicable to the uniform media, constant current and electric field. From the Ohm’s Law, we know the relevance and difference between circuit theory and electromagnetic theory.
Electromagnetic Fields and Waves
Chapter 11 Constant Current in Conductor
王世伟 (Raymond Wong)
Associate Prof. School of Electronic and Information Engineering South China University of Technology TEL: 22236201-604 Email:eewsw@
J E －Conductivity导电率（S/m，or 1/m）
This formula is called the Differential Form of the Ohm’s Law. If the formula is applied in a thin wire with evenly distributed Conductivity and evenly distributed electric field and current in cross-section of the wire, we get that:
The existence of the constant current in the conductor means
there are existence of magnetic field inside and outside the conductors.
Ohm‘s欧姆定律 Law in Conductive Media
If the constant current exists in a conductor circuit, the circuit
should have a electric field to push the movement of the charge, and the electric field is produced by the power supply/source.
called constant current, i.e., direct-current 直 流 (D.C.). The current varying with time is called time-varying current, i.e., alternating-current交流(A.C.).
Ohm's Law in Conductive Media
Ohm’s has a big significance in the developing history of
electricity, but it didn’t get attention of the German scientific community. Until 1841, the British Royal Society affirmed his achievement, and awarded the Copley Award by the British Royal Society.
J ( E E)
Called: Full Ohm's Law

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External source
Ohm's Law in Conductive Media
Discovery of the Ohm’s Law
In 1826, G.S Ohm（1789－1854）discovered the Ohm’s Law. At that time, he was a teacher of a middle school in German, Inspired by the Heat Conduction Theory discovered by Fourier, that is the heat flow between two points in the thermal rod is proportional to the temperature difference, he guesses that the current between two points in the conductor is proportional to the voltage, and he called the voltage as electric tension.