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Physics 2113
Jonathan Dowling
Lecture 31: MON 10 NOV
Review Session : Midterm 3
EXAM 03: 6PM TUE 11 NOV in Cox Auditorium
The exam will cover: Ch.27 through Ch.30
The exam will be based on: HW08 – HW11.
The formula sheet for the exam can be found here:
http://www.phys.lsu.edu/classes/fall2014/phys2113/downloads/FormulaSheetTest3.pdf
You can see examples of old exam IIIs here:
http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys2102/Phys2102OldTests/
Circuits
i = dq/dt
Junction rule
DC Circuits
Loop rule
V = iR
P = iV
Single loop
Multiloop
Resistors vs Capacitors
Resistors
Key formula: V=iR
Capacitors
Q=CV
In series: same current
Req=∑Rj
same charge
1/Ceq= ∑1/Cj
In parallel: same voltage
1/Req= ∑1/Rj
same voltage
Ceq=∑Cj
Resistors
in Series and in Parallel
• What’s the equivalent resistance?
• What’s the current in each resistor?
• What’s the potential across each resistor?
• What’s the current delivered by the battery?
• What’s the power dissipated by each resisitor?
Circuits: Checkpoints, Questions
Problem: 27.P.018. [406649]
Figure 27-33 shows five 5.00 resistors.
(Hint: For each pair of points, imagine that a battery is connected
across the pair.)
Fig. 27-33
(a) Find the equivalent resistance between points F and H.
(b) Find the equivalent resistance between points F and G.
Slide Rules:
You may bend the wires but not break them.
You may slide any circuit element along a wire
so long as you don’t slide it past a three (or
more) point junction or another circuit
element.
Problem: 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 16.0
µC?
Magnetic Forces and Torques
v
r=
F
L
mv
qB
Top view
t net = iAB sin q
Side view
CFnet = 0
C
(28-13)
U = mB
U = -m B
(28-14)
Ch 28: Checkpoints and Questions
Circular Motion:
v
F
r
B into blackboard.
Since magnetic force is perpendicular to motion,
the movement of charges is circular.
2
v
out
Fcentrifugal
= ma = mrw 2 = m
r
in
Fmagnetic
= qvB
FB = FC
mv
® qv B =
r
2
mv
Solve : r =
qB
In general, path is
a helix (component of v parallel to
field is unchanged).
.
electron
C
.
r
mv
r=
qB
v qB
w= =
r m
2pr 2pmv 2pm
Tº
=
=
v
qBv
qB
1 qB
f º =
T 2pm
Radius of Circlcular Orbit
Angular Frequency:
Independent of v
Period of Orbit:
Independent of v
Orbital Frequency:
Independent of v
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?
= - m Bcosq
B
Highest Torque:
 = ±90° sin = ±1
Lowest Torque:
 = 0° & 180° sin = 0
 = 180°
–cos = +1
 = 0°
–cos = –1
Right Hand Rule: Given Current i Find Magnetic Field B
Checkpoints/Questions
Magnetic field?
Force on each wire due to
currents in the other wires?
Ampere’s Law: Find Magnitude of ∫B∙ds?
Right Hand Rule: Given Current i Find Magnetic Field B
The current in wires A,B,D is out of the
page, current in C is into the page. Each wire
produces a circular field line going through
P, and the direction of the magnetic field for
each is given by the right hand rule. So, the
circles centers in A,B,D are
counterclockwise, the circle centered at C is
clockwise. When you draw the arrows at the
point P, the fields from B and C are pointing
in the same direction (up and left).
Right Hand Rule & Biot-Savart: Given i Find B
A length of wire is formed into a closed circuit with radii a and b, as
shown in the Figure, and carries a current i.
(a) What are the magnitude and direction of B at point P?
m 0 if
B=
4pR
(b) Find the magnetic dipole moment of the circuit.
 =NiA
Lenz’s Law
Induction and Inductance
• Faraday’s law: E = - dF B
dt
or
• Inductance: L=N/i
– For a solenoid: L= 0n2Al= 0N2A/l
• Inductor EMF: EL= -L di/dt
• RL circuits: i(t)=(E/R)(1–e–tR/L) or i(t)=i0e–tR/L
• RL Time Constant:  = L/R Units: [s]
• Magnetic energy: U=Li2/2 Units: [J]
• Magnetic energy density: u=B2/2m0 Units: [J/m3]
i
Changing B-Flux Induces EMF
Flux Up
RL Circuits
Flux Down
tL = L / R
E
iup ( t ) = (1- e-t /t L )
R
1 2
U B ( t ) = Li
2
1 E2
-t /t L 2
= L 2 (1- e
)
2 R
To find E L walk the loop : +E + VR + E L = 0
E L = -E - VR = -E - ( -iR )
éE
ù
= -E + ê (1- e-t /t L ) ú R
ëR
û
E L = -E e-t /t L
E -tR/L
idn ( t ) = e
R
1 2
U B ( t ) = Li
2
2
1 E -2tR/L
= L 2e
2 R
Walk the loop!
E L = -VR = -iR
E L = -E e-t /t L
RL Circuits
E/2
t=?
Make or Break?
At t=0 all L’s make breaks so throw out all
loops with a break and solve circuit.
At t=∞ all L’s make solid wires so replace L’s
with wire and solve circuit.
Checkpoints/Questions
Magnitude/direction of induced current?
Magnitude/direction of magnetic field inducing current?
Magnitude of induced emf/current?
Given |∫E∙ds| , direction of
magnetic field?
Given B, dB/dt, magnitude of
electric field?
Current inducing EL?
Largest L?
Current through the battery?
Time for current to rise 50% of max value?
Largest current?
R,L or
2R,L or
R, 2L or
2R,2L?
When the switch is closed, the
inductor begins to get fluxed up,
and the current is
i=(E/R)(1-e–t/τ).
When the switch is opened, the
inductors begins to deflux.
The current in
this case is then
i= (E/R) e–t/τ