From last time…

1. From last time… A B Electric fields Electric field lines Physics 208 Lecture 7

2. Alternate exam time for students with class conflicts: Wed. Feb. 20, 2:30-4Wed. Feb. 20, 6-7:30 To attend alternate exam, you must email me with 1) your conflict, 2) which exam Exam 1 , Wed. Feb. 20, 5:30-7 pm Covers Chap. 21.5-7, 22-23,25-26 + lecture, lab, discussion, HW 8 1/2 x 11 handwritten note sheet (both sides) allowed Review Group/Quiz (solutions on website). Review lab question sheets. Review sample exams on website. Week5 HW (avail. this Thurs, due Fri. next week) covers exam material. Physics 208 Lecture 7

3. Friday Guest Lecture Prof. Thad Walker UW Physics “Holography” Physics 208 Lecture 7

4. Superposition of electric fields • Electric field from a point charge: • From a set of point charges: • Superpose E-fields from individual charges Physics 208 Lecture 7

5. Charge Densities • Volume charge density: when a charge is distributed evenly throughout a volume •  = Q / V dq =  dV • Surface charge density: when a charge is distributed evenly over a surface area •  = Q / A dq = dA • Linear charge density: when a charge is distributed along a line •  = Q / dq =  d Physics 208 Lecture 7

6. Infinite line of charge + + + + + + + + + + + + + + + + + + + An infinite line of charge has a uniform charge density  Coulombs / meter. What direction is the electric field at point x? B. C. x A. D. E. Physics 208 Lecture 7

7. E-field: infinite line of charge r x y • Charge density Coulombs/meter + + + + + + + + + + + + + + + + + + + + Physics 208 Lecture 7

8. Add all these up • Units? Physics 208 Lecture 7

9. Finite line of charge + + + + + + + + + + + + + + + + + + + + C D B What direction is the E-field above the end of the line charge? E A Physics 208 Lecture 7

10. Ring of uniform positive charge y Which is the graph of the field on the axis? A) B) C) D) E) x z Physics 208 Lecture 7

11. Quick quiz We have an infinite sheet of charge of uniform charge density . The electric field increases with distance from plane decreases with distance from plane is independent of distance from plane changes direction with distance from plane Physics 208 Lecture 7

12. E-field of plane of charge Surface charge density • Text does this as adding up rings of charge. Physics 208 Lecture 7

13. Electric fields and forces • Original definite of E-field was(Coulomb Force) / charge • E-field produced force on charged particle. Physics 208 Lecture 7

14. Quick Quiz A negative charge in outer space is in a uniform E-field that points to the right. What is the motion of the particle? Fe - Uniform E A) Moves right at constant speed B) Moves left at constant speed C) Remains stationary D) Accelerates to the left E) None of the above Physics 208 Lecture 7

15. Force on charged particle • Electric field produces force qE on charged particle • Force produces an acceleration a = FE / m • Uniform E-field (direction&magnitude) produces constant acceleration • Positive charge accelerates in direction of the field • Negative charge accelerates in direction opposite the electric field Physics 208 Lecture 7

16. Electron in a Uniform Field • The electron is projected horizontally into a uniform electric field • The electron undergoes a downward acceleration • It is negative, so the acceleration is opposite E • Motion is parabolic while between the plates Physics 208 Lecture 7

17. Fe Fluid - Uniform E Quick Quiz A negative charge is released in a fluid with a uniform E-field that points to the right. The fluid imparts a force proportional to and opposite to the velocity What is the motion of the particle? A. Accel left continuously B. Accel left, then moves at const. speed C. Accel left, then slows to stop D. Accel left, then turns around E. None of the above Physics 208 Lecture 7

18. Motion of charged particle • If no other forces, positive charge accelerates in direction of E-field. • But many systems have drag forces (e.g. molecules in a liquid, etc) • Drag force is complex, but usually depends on velocity. • Particle reaches terminal velocity, determined by force balance Physics 208 Lecture 7

19. Application: Gel Electrophoresis Steady state: FE+FD=0 • Charged macromolecules in ‘gel’ with applied E-field • Electric force: FE = qEDrag force: FD ~ -cv • v = qE / c • Speed depends on charge and drag (molecule size) • Sometimes too complex to interpret • Protein electrophoresis:soak in detergent to give proteinsall the same charge density. • Result, small proteins move faster Physics 208 Lecture 7

20. Isoelectric focusing • Separate macromolecules by charge, not size • Macromolecules put in solution of linearly varying pH • Electric field applied • Charge on molecule depends on local pH • Molecules move until no more force - at their isoelectric point Physics 208 Lecture 7

21. Quick Quiz An electric dipole is in a uniform electric field as shown. The dipole Dipole accelerates left accelerates right stays fixed accelerates up none of the above Physics 208 Lecture 7

22. Electric torque on dipoles • Total torque has magnitude • Dipole moment has magnitude • Torque on dipole in uniform field Physics 208 Lecture 7

23. Dipole in non-uniform field + • A permanent dipole is near a positive point charge in a viscous fluid. The dipole will rotate CW & move toward charge rotate CW & move away rotate CCW & move toward rotate CCW & move away none of the above Physics 208 Lecture 7