1. Physics 213 General Physics Lecture 3

2. 2 Last Meeting: Electric Field, Conductors Today: Gauss’s Law, Electric Energy and Potential

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

4. 4 Demo (Flux)  Pivoting rectangle

5. Electric Flux Through Angled Surfaces

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7. 7 Demo  Styrofoam ball with toothpicks

8. 8 Gauss’ Law

9. Gauss’ Law states that the electric flux outward through any closed surface is equal to the net charge Q inside the surface divided by ε o ε o is the permittivity of free space and equals 8.85 x 10 -12 C 2 /Nm 2 The area in Φ is an imaginary surface, a Gaussian surface, it does not have to coincide with the surface of a physical object

10. 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 zero

11. 11 Electric Field of a Nonconducting Plane Sheet of Charge

12. 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

13. 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

14. Conductors in Electrostatic Equilibrium When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium An isolated conductor has the following properties: 1. The electric field is zero everywhere inside the conducting material. 2. Any excess charge on an isolated conductor resides entirely on its surface. 3. The electric field just outside a charged conductor is perpendicular to the conductor’s surface. 4. The charge accumulates at locations where the radius of curvature of the surface is smallest (that is, at sharp points).

15. Property 3 The electric field just outside a charged conductor is perpendicular to the conductor’s surface Consider what would happen it this was not true The component along the surface would cause the charge to move It would not be in equilibrium

16. 16 In a conductor electrons are free to move. If a conductor is placed into E, a force F = -eE acts on each free electron. Soon electrons will pile up on the surface on one side of the conductor, while the surface on the other side will be depleted of electrons and have a net positive charge. These separated negative and positive charges on opposing sides of the conductor produce their own electric field, which opposes the external field inside the conductor and modifies the field outside. Electrons inside the conductor experience no force.

17. Lightning Rod Effect Any excess charge moves to its surface The charges move apart until an equilibrium is achieved The amount of charge per unit area is greater at the flat end The forces from the charges at the sharp end produce a larger resultant force away from the surface Why a lightning rod works

18. 18 Demo  Van de Graaff Generator

19. Van de Graaff Generator Charge is transferred to the dome by means of a rotating belt

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21. Work and Potential Energy There is a uniform field between the two plates As the charge moves from A to B, work is done on it W = Fd=q E x (x f – x i ) ΔPE = - W = - q E x  x Only for a uniform field

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