EE 307 Chapter 5 - Electric Fields in Materials

EE 307 Chapter 5 - Electric Fields in Materials - ECE 307...

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Unformatted text preview: ECE 307: Electricity and Magnetism Spring 2010 Instructor: J.D. Williams, Assistant Professor Electrical and Computer Engineering University of Alabama in Huntsville 406 Optics Building, Huntsville, Al 35899 Phone: (256) 824-2898, email: [email protected] Course material posted on UAH Angel course management website Textbook: M.N.O. Sadiku, Elements of Electromagnetics 4 th ed . Oxford University Press, 2007. Optional Reading: H.M. Shey, Div Grad Curl and all that: an informal text on vector calculus, 4 th ed . Norton Press, 2005. All figures taken from primary textbook unless otherwise cited. 8/11/2010 2 Chapter 5: Electric Fields in Material Space • Topics Covered – Properties of Materials – Convection and Conduction Currents – Conductors – Polarization in Dielectrics – Dielectric Constant and Strength – Linear, Isotropic, and Homogeneous Dielectrics – Continuity Equation and Relaxation Time – Boundary Conditions • Homework: 9, 12, 17, 19, 22, 23, 24, 28, 32, 33, 34, 35, 37 All figures taken from primary textbook unless otherwise cited. 8/11/2010 3 Convection and Conduction Currents • Current (in amperes) through a given area is the electric charge passing through the area per unit time • Current Density is the amount of current flowing through a surface (amperes/m 2 ), or the current through a unit normal area at that point • Depending on how the current is produced, there are different times of current density – Convection current density – Conduction current density – Displacement current density (Chapter 9) • Current generated by a magnetic field dt dQ I = S I J ∆ ∆ = ∫ ⋅ = s S d J I 8/11/2010 4 Convection Current Density • Convection current density – Does not involve conductors and does not obey Ohm’s law – Occurs when current flows through an insulating medium such as liquid, gas, or vacuum y v v Su t y S t Q I ∆ = ∆ ∆ ∆ = ∆ ∆ = ∆ ϕ ϕ u J u S I J v y v y ϕ ϕ = = ∆ ∆ = 8/11/2010 5 Conduction Current Density • Conduction current density – Current in a conductor – Obeys Ohm’s law • Consider a large number of free electrons traveling in a metal with mass (m), velocity (u), and scattering time (time between electron collisions), τ . • The carrier density is determined by the number of electrons, n, with charge, e • Conduction current density can then be calculate as • Where σ is the conductivity of the conductor • This relationship between current concentration and electric field is known as Ohm’s Law E E m ne u J ne u m E q F v v σ τ ϕ ϕ τ = = = − = = − = 2 8/11/2010 6 Conductors • Conductors are materials with an abundance of free moving charges • Convention states that when an electric field is applied to a conductor, the positive free charges are pushed along the same direction of the applied field, while the negative charges move in the opposite direction • The free charges do two things...
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EE 307 Chapter 5 - Electric Fields in Materials - ECE 307...

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