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Introduction to Electric Fields and Materials

This lecture introduces materials that contain charged particles and their response to applied electric fields. It covers conductors, semiconductors, and dielectrics, and explores the concept of current in free space. The lecture also defines convection current, current density, and continuity current equation.

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Introduction to Electric Fields and Materials

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  1. LECTURE 12 FIELDS AND MATERIALS

  2. INTRODUCTION • In our discussion of electric field thus far, we considered the medium to be free space and source to be static charges. • We shall now introduce materials. Contain charged particles that respond to applied field Conductor Depending on their response, they may be classified as Semiconductor Dielectric

  3. APPROACH Moving charges Study moving charges in free space. Conductivity (s) Conductors Ohm’s law Resistance from field theory Conductor properties under static conditions Conductor – Free space boundary conditions Dielectrics Dielectric properties under static conditions Dielectric - dielectric boundary conditions Applications Capacitor

  4. MOVING CHARGES • OBJECTIVES • To introduce concept of current in free space. • To define convection current and convection current density. • To explain in your own words the concept of continuity current equation.

  5. DEFINITION Long cylinder of rv x Ux E dS dQ dx Current is defined as the movement of charge through a given surface and is equal to the coulombs per second through that surface. Exploded view of sample dQ

  6. MATHEMATICAL MODEL Convection current Divide by dS, introducing current density Written in general vector form Convection current density

  7. Consider a material where both positive and negative charges exist E +ve -ve x P At point P, current density Total current

  8. EXAMPLE • The vector current density is given as (i) Find J at r = 3, q = 0, f = p. (ii) Find the total current passing through the spherical cap r = 3, 0 < q < 200, 0 < f < 2p, in the direction.

  9. CONTINUITY OF CURRENT EQUATION Divergence theorem The point form of the continuity of the current equation

  10. EXAMPLE • Assume that an electron beam carriers a total current of – 500 mA in the positive z direction, and has a current density Jz that is not a function of r or f in the region 0 < r < 10-4 m and is zero for r > 10-4 m. If the electron velocities are given by vz = 8 x 107z m/s, calculate rv at r = 0 and z = : (i) 1 mm; (ii) 2 cm; (iii) 1 m.

  11. THANK YOU QUESTIONS & ANSWERS

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