Resistance and Ampere's law Apr. 11, 2007

+ Relation between electron and hole concentrations: where is the intrinsic concentration and is a constant for fixed temperature
P-type and n-type

+ Power density () = (Sect. 4.4)

+ Resistance (Sect. 4.6)

+ Conservation of charge continuity equation
(Sect. 4.3)
For steady current
Decay time or relaxation time in a lossy dielectric:
For homogeneous medium . That is the RC time constant!
Example 4.3: Discharge in a lossy dielectric and its relation to RC circuit
Example 4.4: Resistance between the inner radius and outer radius of a cylinder

+ Ampere's law (Sect 5.2):
Note: is the external current (i.e. from a power source) enclosed by the path of integration
Applications: find for a given current for INFINITELY line or plane or object without ends, e.g. infinite long wire, infinite sheet, long coaxial cable, long solenoid, toroid.
Choose a path with constant = I / (path length)
Example 4.6: Application of Ampere's law

+ Maxwell's equation for static field:
Applications for Maxwell's equation: given find
Example 4.7: Differential form of Ampere's law

+ Magnetic flux density (T); permeability and for free space
Example 4.8: Magnetic field of a toroid
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HW #19 Due 4/19/07

1. The results in HW18 problem 3 can be useful in determining the placement of power line. A 48KV line has a radius of 3cm and is 11m above ground (0V potential). Consider the line as the inner cylinder of the cylindrical capacitor and the ground as the outer cylinder of the cylindrical capacitor in HW18 problem 3. a) From the IEEE standard for the field safety on web page, find the maximum permissible exposure (MPE) for uncontrolled environments. Use the value for the lowest frequency since there is no data for available for power line frequency. b) Find the potential distribution as a function of radial distance from the line. c) Find the electrical field 2m (the height of a person) above ground. Will this height of the line be safe according to MPE limit. d) Repeat calculations in b) and c) if the line is 14m above ground. Will this height be safe?
2. Consider a person is protected by a ground aluminum clothing. Approximate the human body as a cylinder with length of 2m and radius of 0.4m. Approximate the clothing as a aluminum foil surrounding the cylindrical with thickness of 0.75mm. a) Find the resistance of the human body, the resistance of the aluminum clothing and total resistance. Notice conductivity of human body is 0.2 S/m and that of aluminum is S/m. b) Assuming current density is uniform in each region and 15A of current passing through the total resistance. Find J, E and power density in both human body as well as clothing.
3. For the cylindrical capacitor in HW 18 problem 2, a) find the resistance between and if the concentric cylinders with lossy dielectric: has , , has , and is , and b) draw the equivalent RC circuit for the lossy capacitor.
Extra-credit
P.4-3a, P.4-4a (page 167)