1. Exam 2: Review Session CH 24–28
Physics 2102
Jonathan Dowling
Physics 2102
Exam 2: Review Session
CH 24–28
Some links on exam stress:

2. Exam 2
(Ch24) Sec.11 (Electric Potential Energy of a System of Point Charges); Sec.12 (Potential of Charged Isolated Conductor)
(Ch 25) Capacitors: capacitance and capacitors; caps in parallel and in series, dielectrics; energy, field and potential in capacitors.
(Ch 26) Current and Resistance: current, current density and drift velocity; resistance and resistivity; Ohm’s law.
(Ch 27) Circuits: emf devices, loop and junction rules; resistances in series and parallel; DC single and multiloop circuits, power; RC circuits.
(Ch 28) Magnetic Fields: F=vxB, Right Hand Rule, Circular Motion, Force on Wire, Magnetic Dipole.

3. Potential Energy of a System of Charges

4. Potential Energy of A System of Charges
4 point charges (each +Q) are connected by strings, forming a square of side L
If all four strings suddenly snap, what is the kinetic energy of each charge when they are very far apart?
Use conservation of energy:
Final kinetic energy of all four charges = initial potential energy stored = energy required to assemble the system of charges +Q +Q +Q +Q
Do this from scratch! Don’t memorize the formula in the book!
We will change the numbers!!!

5. Potential Energy of A System of Charges: Solution+Q +Q
No energy needed to bring in first charge: U1=0
Energy needed to bring in 2nd charge: +Q +Q
Energy needed to bring in 3rd charge =
Total potential energy is sum of all the individual terms shown on left hand side =
Energy needed to bring in 4th charge =
So, final kinetic energy of each charge =

6. (24-19)

7. Capacitors E = s/e0 = q/Ae0 E = V d q = C V C = e0A/d C = k e0A/d
C=e0ab/(b-a)

8. Current and resistance
i = dq/dt
Junction rule
R = rL/A
V = i R
E = J r
r = r0(1+a(T-T0))

9. DC Circuits
Loop rule
Multiloop
Single loop
V = iR
P = iV

10. Resistors and Capacitors
Resistors Capacitors
Key formula: V=iR Q=CV
In series: same current same charge
Req=∑Rj /Ceq= ∑1/Cj
In parallel: same voltage same voltage
1/Req= ∑1/Rj Ceq=∑Cj

11. Capacitors and Resistors in Series and in Parallel
What’s the equivalent resistance (capacitance)?
What’s the current (charge) in each resistor (capacitor)?
What’s the potential across each resistor (capacitor)?
What’s the current (charge) delivered by the battery?

12. RC Circuits
Time constant: RC
i(t)=dq/dt

13. Capacitors: Checkpoints, Questions

14. Problem 25-21
When switch S is thrown to the left, the plates of capacitor 1 acquire a potential V0. Capacitors 2 and 3 are initially uncharged. The switch is now thrown to the right. What are the final charges q1, q2, and q3 on the capacitors?

17. Current and Resistance: Checkpoints, Questions

18. Problem 26-56
A cylindrical resistor of radius 5.0mm and length 2.0 cm is made of a material that has a resistivity of 3.5x10-5 Wm. What are the (a) current density and (b) the potential difference when the energy dissipation rate in the resistor is 1.0W?

20. Circuits: Checkpoints, Questions

21. Problem: 27.P.018. [406649]
Figure shows five 5.00 resistors.
(Hint: For each pair of points, imagine that a battery is connected across the pair.)
Fig
(a) Find the equivalent resistance between points F and H.
(b) Find the equivalent resistance between points F and G.

23. Proble: 27.P.046. [406629]
In an RC series circuit, E = 17.0 V, R = 1.50 M, and C = 1.80 µF.
(a) Calculate the time constant.
(b) Find the maximum charge that will appear on the capacitor during charging.
(c) How long does it take for the charge to build up to 10.0 µC?

25. Magnetic Forces and Torquesv F L

26. C
Top view
Side view
(28-13)

27. (28-14)

28. Ch 28: Checkpoints and Questions

29. Problem: 28.P.024. [566302]
In the figure below, a charged particle moves into a region of uniform magnetic field , goes through half a circle, and then exits that region. The particle is either a proton or an electron (you must decide which). It spends 160 ns in the region.
(a) What is the magnitude of B?
(b) If the particle is sent back through the magnetic field (along the same initial path) but with 3.00 times its previous kinetic energy, how much time does it spend in the field during this trip?