Exam 2 covers Ch. 27-32, Lecture, Discussion, HW, Lab

1. Exam 2 covers Ch. 27-32,Lecture, Discussion, HW, Lab Exam 2 is Wed. Mar. 26, 5:30-7 pm, 2103 Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308) • Chapter 27: Electric flux & Gauss’ law • Chapter 29: Electric potential & work • Chapter 30: Electric potential & field • Chapter 28: Current & Conductivity • Chapter 31: Circuits • Chapter 32: Magnetic fields & forces • (exclude 32.6,32.8,32.10)

2. Electric flux • Suppose surface make angle  surface normal Component || surface Component  surface Only  component‘goes through’ surface • E = EA cos  • E =0 if E parallel A • E = EA (max) if E  A • Flux SI units are N·m2/C

3. Gauss’ law • net electric flux through closed surface = charge enclosed / 

4. Field outside uniformly-charged sphere • Field direction: radially out from charge • Gaussian surface: • Sphere of radius r • Surface area where • Value of on this area: • Flux thru Gaussian surface: • Charge enclosed: • Gauss’ law:

5. Electric potential energy Work is Force x distance (taking into account cosθ between 2 vectors!) >0 since they repel! potential energy increases If opposte charges they attract => W <0 and potential energy decreases

6. Electric Potential Electric potential energy per unit chargeunits of Joules/Coulomb = Volts Example: charge q interacting with charge Q Electric potential energy Electric potential of charge Q Q source of the electric potential, q ‘experiences’ it

7. Example: Electric Potential y Calculate the electric potential at B B x d d2=4 m -12 μC +12 μC A - + Calculate the electric potential at A d1=3 m 3 m 3 m Calculate the work YOU must do to move a Q=+5 mC charge from A to B.

8. Work and electrostatic potential energy electric potential energy of the system increases −3μC −1μC −2μC Question: How much work would it take YOU to assemble 3 negative charges? Likes repel, so YOU will still do positive work! A. W = +19.8 mJ B. W = -19.8 mJ C. = 0 q3 5 m 5 m q2 q1 5 m

9. Potential from electric field • Electric field can be used to find changes in potential • Potential changes largest in direction of E-field. • Smallest (zero) perpendicular to E-field V=Vo

10. Electric Potential and Field • Uniform electric field of E = 4i+3j N/C • Points A at 2m and B at 5m on the x axis. • What is the potential difference VA - VB? A(2,0) B(5,0) 0 x(m) E = 4i N/C A) -12V B) +12V C) -24V D) +24V

11. Capacitors +Q -Q Area A d Conductor: electric potential proportional to charge: C = capacitance: depends on geometry of conductor(s) Example: parallel plate capacitor Energy stored in a capacitor:

12. Isolated charged capacitor • Plate separation increased • The stored energy • Increases • Decreases • Does not change Stored energy A) B) C) q unchanged because C isolated q is the same E is the same = q/(Aε0) ΔV increases = Ed C decreases U increases

13. Conductors, charges, electric fields • Electrostatic equilibrium • No charges moving • No electric fields inside conductor. • Electric potential is constant everywhere • Charges on surface of conductors. • Not equilibrium • Charges moving (electric current) • Electric fields inside conductors -> forces on charges. • Electric potential decreases around ‘circuit’

14. Electric current L • Average current: • Instantaneous value: • SI unit: ampere1 A = 1 C / s n = number of electrons/volume n x AL electrons travel distance L = vd Δt Iav = ΔQ/ Δt = neAL vd /L • Current density J= I/A = nqvd (direction of + charge carriers)

15. Resistance and resistivity • Ohm’s Law: ΔV = R I (J = σE or E = ρJ) • ΔV = EL and E = ρ J => ρ I/A = ΔV/L • R = ρL/A Resistance in ohms (Ω)

16. Current conservation I2 I1 I3 I1=I2+I3 I1 I3 I2 I1+I2=I3 Iin Iout Iout = Iin

17. Resistors in Series and parallel R1 R2 • Parallel • V1 = V2 = V • Req = (R1-1+R2-1)-1 • Series • I1 = I2 = I • Req = R1+R2 I1+I2 I R1 R1+R2 I = = I1 I2 I R2 2 resistors in series: R  L Like summing lengths

18. Quick Quiz How does brightness of bulb B compare to that of A? B brighter than A B dimmer than A Both the same Battery maintain constant potential difference Extra bulb makes extra resistance -> less current

19. Quick Quiz What happens to the brightness of bulb B when the switch is closed? Gets dimmer Gets brighter Stays same Something else Battery is constant voltage,not constant current

20. Quick Quiz What happens to the brightness of bulb A when the switch is closed? Gets dimmer Gets brighter Stays same Something else

21. Capacitors as circuit elements • Voltage difference depends on charge • Q=CV • Current in circuit • Q on capacitor changes with time • Voltage across cap changes with time

22. R R RC Circuits C C ε Start w/uncharged CClose switch at t=0 Start w/charged CClose switch at t=0

23. Capacitors in parallel and series • ΔV1 = ΔV2 = ΔV • Qtotal = Q1 + Q2 • Q1=Q2 =Q • ΔV = ΔV1+ΔV2 • 1/Ceq = 1/C1 + 1/C2 Ceq = C1 + C2

24. Calculate the equivalent Capacitance C1 C2 C3 V C4 parallel C1, C23, C4 in series C1 = 10 μF C2 = 20 μF C3 = 30 μF C4 = 40 μF V = 50 Volts

25. RC Circuits What is the value of the time constant of this circuit? A) 6 ms B) 12 ms C) 25 ms D) 30 ms

26. Magnetic fields and forces I • Magnetic force on current-carrying wire B Magnetic force on moving charged particle I B • Magnetic torque on current loop

27. Effect of uniform magnetic field • Effect of uniform B-field on charged particle • If charged particle is not moving - no effect • If particle is moving:force exerted perpendicularto both field and velocity vector ‘cross product’

28. F Lorentz force Electron moves in plane of screen the page. B- field is in the plane of screen to the right. Direction of instantaneous magnetic force on electron is A) toward the top of the page B) into the page C) toward the right edge of the page D) out of the page B v electron

29. Trajectory in Constant B Field x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x B v q v F F • Charge enters B field with velocityshown. (vB) • Force is always ^ to velocity and to B. • Path is a circle. • Radius determined by velocity:

30. Current loops & magnetic dipoles • Current loop produces magnetic dipole field. • Magnetic dipole moment: Area of loop current direction magnitude Effect of uniform magnetic field Magnetic field exerts torqueTorque rotates loop to align with

31. τ τ μ μ Question on torque Which of these loop orientations has the largest magnitude torque? (A) a(B) b(C) c a b c Answer: (c). all loops enclose same area and carry same current ⇒ magnitude of μ is the same for all. (c) μ upwards, μ⊥B and τ = μB. (a), τ= 0 (b) τ = μBsinθ