19. Electric Forces and Electric Fields

1. 원인 결과 • Ancient Period ---- Charge • Oested ---- Current vs Magnetic Field • Faraday ---- Electromagnetism --- Phenomenology • Maxwell ---- Electromagnetism 의 완성 19. Electric Forces and Electric Fields • Newton’s Law 1. 관성의 법칙 2. 운동의 법칙 3. 작용 반작용의 법칙 • Forces in Nature Mass 1. Gravitational Force 2. Electromagnetic Force 3. Strong Force 4. Weak Force Charge 19-1. Historical Overview Maxell’s Equations cf) Newton’s Law

2. ++ : Repulsive –– : Repulsive +– : Attractive – + : Attractive 19-2. Properties of Electric Charges • Two kinds of charges (positive and negative) in Nature • The force : proportional to the inverse square of the separation.  Coulomb’s Law • Charge : Conserved & Quantized Sum of Charges = 0 Charge: Electron has charge of -e.

3. Metals (Conductors) : free movement of electric charges e.g. Fe, Cu, Au, Ag, ··· Insulators : no free movement of electric charges e.g. Rubber, Ceramic, Cotton, ··· Conductor Grounded 19-3. Insulators and Conductors • Materials Semiconductor : Insulator but the electric charges can be created either by the thermal energy or by dopings e.g. Si, GaAs, ··· • Charging by Induction Charges are uniformly distributed at the surface of conductors. Induced Charge due to polarization in insulators.

4. 19-4. Coulomb’s Law • Gravitational Force : between two massive objects G = 6.6710-11N·m2/kg2 Always attractive • Electrical Force (Coulomb’s Law) : between two charged particles ke= 8.9910-11N·m2/C2 Permittivity of vacuum Charge of an electron or proton : |e| = 1.602  10-19 C = (6.25  1018)-1C • Vector notation of Coulomb’s Law : Newton’s third law The magnitude is the same but the direction is opposite.

5. + – q1 q2 - + q4 q3 e - + p • Coulomb Force due to many charges Vector Sum Example 19.2 Hydrogen Atom Average separation r= a0 = 5.3  10-11m |e| = 1.60  10-19C mp = 1.67  10-27kg , me = 9.11  10-31kg Electrical force Gravitational force

6. 19-5. Electric Fields Electric Field : Electric force per unit charge acting on a testcharge SI unit : N/C For a point charge q: Electric force on a test charge Electric Field: Force  Field : Often much easier to describe the physical phenomena For a group of charges : Vector sum Electric Field:

7. Example 19.3: Electric Field of a dipole (p677) For r >> a: 19-7. Motion of Charged Particles in a Uniform Electric Field

8. , , , • Electric Field Due to Continuous Charge Distributions Electric field at P due to charge Dq Total Electric field at P qi 0 for the continuous charge distributions: • Charge Density for uniform distributions - Charge desity , r : Charge per unit volumes - Surface charge density, s : Charge per unit area - Linear charge density, : Charge per unit length

9. Example 19.4 Electric Field due to a Charged Rod Total Charge Q Linear charge density If d >> l, : like a point charge

10. Example 19.5 Electric Field due to an Uniform Ring Charge Total Charge Q Linear charge density If x = 0, E = 0. If x >> a, : like a point charge

11. 19-6. Electric Field Lines • Electric Field lines : Visualize the electric field patterns 1. E is tangent to the electric field lines 2. Strength of E  the number of lines per unit area • Rules for drawing Electric field lines 1. Beginon positive charges and terminate on negative charges. 2. The number of lines  the magnitude of charges 3. No two lines cross each other

12. 19-8. Electric Flux Electric Flux F :  the number of the electric field lines through a surface Electric Flux Fis defined as :Directed to the surface normal Electric flux, DFi, through a small surface DAi A general definition of F :

13. 19-9. Gauss Law • Electric Flux through a closed surface (i) No Charge inside

14. (i) A charge inside S1 S2 For an empirical surface, FCis the same. i.e.FCis independent of the surface contour. • Gauss’s Law The net flux through any closed surface is proportional to the net charge inside of the surface.

15. 19-10. Applications of Gauss’s Law to symmetric charge distributions • Gauss’s law is very useful to determine the electric field due to charge distributions with high degree of symmetries, such as spherical, cylindrical, or long plane shapes. Example 19.7 Electrical Field due to a point charge (p692) Example 19.8 A Spherically Symmetric Charge Distribution Charge density r (a) r >a for r > a

16. (b) r <a for r < a

17. + + + + + + + + + dy y x q Example 19.9 A Cylindrically Symmetric Charge Distribution Example 19.10 A Non-conducting Plane Sheet of Charge (p695) Constant i.e. Uniform field

18. Gauss Surface + + + + + + R + + + + r + + + + + + + + + 19-11. Conductors in Electrostatic Equilibrium • E = 0 inside of Conductors • Excess charges reside entirely on its surface • E field just outside of a conductor surface is perpendicular to the surface and has a magnitude σ/εo. • The σis highest at the surface with the smallest radius of curvature. • Charges freely move inside Conductors. For r < R, For r > R,

19. 19-12. The Atmospheric Electric Field According to the “Field Mill” measurement data in clear weather days, the average E-field on the Earth surface is; E ~ 100 N/C From this we can estimate the average surface charge density of the Earth; σ = Eεo ~ 10-9 C/m2 Or, average total charge on Earth is, Q = σ (4πR2) ~ 5 x 105 C

20. FIELD MILL