Torque on the electric dipole

1. The problem solving session will be Wednesdays from 12:30 – 2:30 (or until there is nobody left asking questions) in FN 2.212

2. Torque on the electric dipole (electric dipole moment from “-” to “+”) Electric field is uniform in space Net Force is zero Net Torque is not zero (torque is a vector) Stable and unstable equilibrium

3. Charge #2 +q Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole. The net electric torque that Charge #1 exerts on the dipole is Charge #1 +q y –q x Charge #3 A. clockwise. B. counterclockwise. C. zero. D. not enough information given to decide

4. Electric field of a dipole A - - + + d A d E-field on the line connecting two charges when r>>d E-field on the line perpendicular to the dipole’s axis General case – combination of the above two

5. Dipole’s Potential Energy E-field does work on the dipole – changes its potential energy Work done by the field (remember your mechanics class?) Dipole aligns itself to minimize its potential energy in the external E-field. Net force is not necessarily zero in the non-uniform electric field – induced polarization and electrostatic forces on the uncharged bodies

6. Chapter 22 Gauss’s Law

7. Charge and Electric Flux Previously, we answered the question – how do we find E-field at any point in space if we know charge distribution? Now we will answer the opposite question – if we know E-field distribution in space, what can we say about charge distribution?

8. Electric flux Electric flux is associated with the flow of electric field through a surface For an enclosed charge, there is a connection between the amount of charge and electric field flux.

9. Calculating Electric Flux Amount of fluid passing through the rectangle of area A

10. - unit vector in the direction of normal to the surface Flux of a Uniform Electric Field Flux of a Non-Uniform Electric Field E – non-uniform and A- not flat

11. Few examples on calculating the electric flux Find electric flux

12. Gauss’s Law

13. Applications of the Gauss’s Law Remember – electric field lines must start and must end on charges! If no charge is enclosed within Gaussian surface – flux is zero! Electric flux is proportional to the algebraic number of lines leaving the surface, outgoing lines have positive sign, incoming - negative

14. Examples of certain field configurations Remember, Gauss’s law is equivalent to Coulomb’s law However, you can employ it for certain symmetries to solve the reverse problem – find charge configuration from known E-field distribution. Field within the conductor – zero (free charges screen the external field) Any excess charge resides on the surface

15. Field of a charged conducting sphere

16. Field of a thin, uniformly charged conducting wire Field outside the wire can only point radially outward, and, therefore, may only depend on the distance from the wire l- linear density of charge

17. s- uniform surface charge density Field of the uniformly charged sphere Uniform charge within a sphere of radius r Q - total charge - volume density of charge Field of the infinitely large conducting plate

18. Charges on Conductors Field within conductor E=0

19. Experimental Testing of the Gauss’s Law