浙江师范大学电磁学课件em41.ppt

Chapter 4
Steady Electric Currents
Sec4-1 Current Density and Ohm’s Law
Sec4-2 Electromotive Force and Kirchhoff’s Law
Sec4-1 Current Density and Ohm’s Law
1. Electric Current
n is the number of charge carriers per unit volume.
Charge density
2. Current density
Definition:
The volume current density J is in the direction of E.
The definition of surface current density is
K is the current per unit length on the surface.
If the current in the surface is perpendicular to dl then
continuity equation
The current flows into the closed surface S
The current flows out the closed surface S
Put together
This equation states that the rate of charge passing outward through the closed surface S is equal to the rate of decrease of charge in the enclosed volume V.
Steady current condition:
Fig. A current tube
Generation: n brunches
4. Ohm’s Law and its local form
The stationary electric field is similar to the electrostatic field:
I = GU G — conductance (siemens)
or
R —resistance(Ω)
International standard of resistance ( 1990):
ΔS
Δl
ΔI
U+ΔU
U
Fig. part of a current tube
is the conductivity (siemens/m) of the conductor.
Example: The space between two metallic coaxial cylinders of radii a and b is filled with a material of resistivity ρ. What is the resistance between the cylinders?
Cross-section of the cylinder
Solution
Work principle of superconducting restrictors
Superconducting restrictor
Resistor