Understanding Electric Forces and Fields: E vs. F | Theoretical Comparison & Applications

1. Chapter 15 Electric Forces and Electric Fields

2. Gauss’s Law Sections 7-9

3. What is the difference between Electric Field (E) and Force (F)? 45 • E factors out the magnitude of the test charge, it only depends on the other charges • E is defined everywhere,F only at one point • Both 1) and 2) • Neither 1) or 2)

4. Review • Corn Field: corn at regularly space intervals • Vector Field: a vector at each point in space • Scalar Field: a number at each point in space • Eg: Temperature

5. Review • Electric Field • Field lines:an easy way to visualize fields • Tangent to E • Density of linesproportional to E field • begin at (+), end at (-) • # of lines proportional to q • lines don’t cross

6. Review • Conductors & Electrostatic equilibrium • E=0 inside a conductor • excess charge lies on outer surface • E is perpendicular to surface • charge is greatest at highest curvature

7. Why are you safe inside a car during a thunder storm? 45 • The rubber tires insulate the car from the ground • Charge cannot come inside the metal shell of the car • The rounded car has a lower charge density • It’s not safe!

8. Millikan Oil-Drop Experiment Millikan Oil-Drop Experiment Found every charge had an integral multiple of e (q = n e) Measured the elementary charge, e = 1.610-19 C Active Figure: The Millikan Oil-Drop Experiment Equilibrium Drag -- Terminal velocity

9. Van de GraaffGenerator An electrostatic generator designed and built by Robert J. Van de Graaff in 1929 Charge is transferred to the dome by means of a rotating belt Limited by ionization of air, which carries charge away Eventually an electrostatic discharge takes place MU28T33

10. Museum of Science, Boston

11. Holifield Radioactive Ion Beam Facility Oak Ridge National Laboratory 25.5 MeV

12. Electric Flux Field lines penetrating an area A perpendicular to the field The product of EA is the flux, Φ (the number of field lines!) In general: ΦE = E A cos θ

13. Electric Flux, cont. • ΦE = E A cos θ • The perpendicular to the area A is at an angle θ to the field • When the area is constructed such that a closed surface is formed, use the convention that flux lines passing into the interior of the volume are negative and those passing out of the interior of the volume are positive

14. Gauss’ Law Gauss’ Law: the electric flux through any closed surface is proportional to the net charge Q inside the surface εo=8.85 x 10-12 C2/Nm2 is the permittivity of free space The area in Φ is an imaginary surface, a Gaussian surface, it does not have to coincide with the surface of a physical object Active Figure: Electric Flux Through an Arbitrary Closed Surface MU29T17

15. Electric Field of a Charged Thin Spherical Shell The calculation of the field outside the shell is identical to that of a point charge The electric field inside the shell is E = 0 MU29T23

16. Electric Field of a Nonconducting Plane Sheet of Charge Total charge Q is uniformly distributed over surface A Charge density σ = Q/A Use a cylindrical Gaussian surface The flux through the ends is EA, no field through the curved part of the surface Note, the field is uniform

17. Electric Field of a Nonconducting Plane Sheet of Charge, cont. The field must be perpendicular to the sheet The field is directed either toward or away from the sheet

18. Parallel Plate Capacitor The device consists of plates of positive and negative charge The total electric field between the plates is given by The field outside the plates is zero

19. What is the total electric flux through the surface of the cubein a constant electric field E? 45 • 0 • E L2 • 6 E L2 • 2 E L2 • 6 E

20. TIME SPACE Maxwell’s Equation #1 or or They all mean the same thing.