1. PHY 2049: Physics II Hopefully all homework problems have been solved. Please see me immediately after the class if there is still an issue. Tea and Cookies: We meet on Wednesdays at 4:00PM for tea and cookies in room 2165.

2. quiz The electric field at a distance of 10 cm from an isolated point particle with a charge of 2×10 −9 C is: A. 1.8N/CB. 180N/CC. 18N/C D. 1800N/CE. none of these

3. Quiz 2 An isolated charged point particle produces an electric field with magnitude E at a point 2m away from the charge. A point at which the field magnitude is E/4 is: A. 1m away from the particle B. 0.5m away from the particle C. 2m away from the particle D. 4m away from the particle E. 8m away from the particle

4. PHY 2049: Physics II Last week Coulomb’s law, Electric Field and Gauss’ theorem Today Electric Potential Energy and Electric Potentials Numerous cases

5. Potential Energy and Potential Force => work => change in K=> change in Potential energy ΔU = U f – U i = -W = - ΔK Work done is path independent. K+U = constant. U = k q 1 q 2 /r : interaction energy of two charges. Sign matters

6. PHY 2049: Physics II Electric Potential V = U/q = -W/q Units of Joules/coulomb = volt 1 eV = e x 1V = 1.6 x 10 -19 J Also V = kq/r V f –V i = -∫E.ds In case of multiple charges, add as a number

7. PHY 2049: Physics II Can you tell the sign of the charge by looking at its behavior over a surface of potentials. Is the speed at the end bigger or smaller than in the beginning. 1.Neg., lower 2.? 3.Pos., higher 4.Neg., higher 5.Pos., higher

8. PHY 2049: Physics II V f -V i = -∫ k q/r 2 dr Choose V i = V (∞)=0 V(r) = kq/r

9. V = kpcosθ/r 2 E = - ∂V/∂s = - Uniformly charged disk V = ??

10. A B C (24 - 6)

11. dq O A (24 - 8)

12. PHY 2049: Physics II

13. . P r dq (24 - 7)

14. (24 - 9)

15. (24 - 10)

16. S A B  V q (24 - 11) S V

17. (24 - 12)

18. A B V V+dV (24 - 13)

19. A B V V+dV (24 - 14)

20. x y O q1q1 q2q2 q3q3 r 12 r 23 r 13 (24 - 15)

21. (24 - 16) O x y  q1q1 Step 1 x y O r 12 q1q1 q2q2  Step 2 Step 3 x y O r 12 r 13 r 23 q1q1 q2q2 q3q3 

22. path A B conductor (24 - 17)

23. (24 - 18)

24. (24 - 19)

25. R (24 - 20)