1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 29: August 5 th 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Gauss’s Law Very long straight cable. 1)Inner cylinder is a conductor. Radius R1=1.00cm Charge per unit length = - 350  C/m 2) Outer cylinder is insulator Outer radius R2= 2.00cm Charge density  = 750x10 -2 C/m 3 Determine E(r) (magn. and direction) Determine surface charge density on Inner cylinder.

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Gauss’s Law Symmetry dictates that the electric field must be pointing radial in or out: E z (r) =0 z Gaussian closed surface Inside the conductor: All the charge is on the surface of the conductor! Inside the conductor (r < R1)

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Gauss’s Law Inside the insulator (R1<r < R2)

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Gauss’s Law Note: The field points inwards up to a certain radius. Then the field is 0 when r is such that the charge on the conductor and the enclosed charge in the insulator Is zero.

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 Gauss’s Law Outside the insulator (R2<r)

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Ray Tracing Convex Mirror C R=0.80m 0.60m

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Ray Tracing C R=0.80m 0.60m F

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Calculation of Image p = + 0.60m (positive because object is real, in front of the mirror) f= - R/2 = - 0.40m (negative because it is a diverging mirror)

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Two Lenses – Characterize the Image

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Image due to Lens 1 O2O2 I 1 =O 2

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Image due to Lens 2 O1O1 O2O2 I2I2

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 We did not get to the following problems in the lecture, but I’ll post them anyhow in case you would like to have some extra practice.

14. Physics for Scientists and Engineers II, Summer Semester 2009 14 Forces on Charges Find the force on 1.0nC charge.

15. Physics for Scientists and Engineers II, Summer Semester 2009 15 Forces on Charges y x

16. Physics for Scientists and Engineers II, Summer Semester 2009 16 Forces on Charges

17. Physics for Scientists and Engineers II, Summer Semester 2009 17 Circuits and Induction 0.500m 5.0V

18. Physics for Scientists and Engineers II, Summer Semester 2009 18 Circuits and Induction 0.500m 5.0V

19. Physics for Scientists and Engineers II, Summer Semester 2009 19 Circuits and Induction

20. Physics for Scientists and Engineers II, Summer Semester 2009 20 Ampere’s Law – calculate B I2I2 I1I1

21. Physics for Scientists and Engineers II, Summer Semester 2009 21 Ampere’s Law – calculate B I2I2 I1I1

22. Physics for Scientists and Engineers II, Summer Semester 2009 22 Ampere’s Law