Review notes for Exam 5 (Serway 31-33)
This is a list of concepts that will be tested, not a list of potential exam problems.
1) Faradays Law of Induction
dΦ B
.
dt
i. State Faraday’s law in plain English without reference to symbols or acronyms and
include the directional information. The electric circulation or emf around a closed
loop is equal to the negative time derivative of the magnetic flux through the loop,
the positive directions of the two being related by the right-hand rule.
ii. It applies even when no loops are present to respond to the emf.
iii. Given B(t), calculate the induced emf around a closed loop.
iv. Given B and a changing loop shape, calculate the induced emf.
v. Given B and a rotating loop, calculate the induced emf.
vi. Qualitatively plot emf(t) generated by a magnetic dipole (e.g. bar magnet) or
magnetic monopole moving through a loop, or for a loop moving into or out of a
field region.
Lenz’s law.
i. A corollary of Faraday’s law pertaining the current generated by magnetic flux
changes though a conducting loop.
ii. Be very sure that you can get the direction right in qualitative problems.
iii. State Lenz’s law in plain English without reference to symbols or acronyms. When
the magnetic flux through a conducting loop changes, the induced current flows in
the direction that creates magnetic flux that opposes the original change in flux.
Motional emf.
i. Emf generated across a simple conducting bar moving in a magnetic field.
ii. For a loop entering a field region, determine the emf generated in terms of motional
emf and in terms of flux change. Show that these two views are equivalent.
Eddy currents: make qualitative assessments of terminal velocity for conducting objects
entering or leaving a field region given B, resistivity, shape, mass, etc.
AC generators and DC motors: be familiar with the relationships amongst I, ω, ε, B, ΦB, N,
A (area), P (power), and τ (torque). Given some of these quantities, be able to calculate the
others.
a. Faradays law of induction: ε = − N
b.
c.
d.
e.
2) Self-inductance.
dI
dt
NΦ
b. Know how to calculate: L =
I
c. Calculate L for simple geometries (solenoid, toroid, with or without magnetic core
material).
a. Know the definition: ε = − L
3) Magnetic field energy
a. Energy stored in an inductor (remember capacitors too)
b. Magnetic field energy density (remember electric fields too)
4) LR circuits
dI
.
dt
Solutions for: I(t) and V(t) across L and R.
Calculate the L/R time constant.
Calculate dI/dt at t = 0 in an LR circuit.
Solve the simple R=0 case to emphasize the importance of understanding the diffeq.
Have a qualitative understanding of inductive kick or flyback.
a. Differential equation: ε = IR + L
b.
c.
d.
e.
f.
5) Free LC oscillations, including damped oscillations.
dI
d 2Q
a. Differential equation: Q / C + L
= Q /C + L 2 = 0.
dt
dt
b. Natural frequency for damped and undamped cases.
c. A resistive term damps the oscillations exponentially in time, shifts the natural frequency,
and always dissipates energy.
d. Have an intuitive knowledge of the LRC/mass-spring analogies in Serway Table 32.1.
6) Driven RLC circuits: any combination or L,R,C.
a. The elements of an RLC circuit have separate voltages but a common current.
dI
dQ
d 2Q
b. Diffeq: ε = Q / C + IR + L
= Q/C + R
+L 2 .
dt
dt
dt
c. Impedance: V/I = Z = R+iX = |Z|eiφ has both magnitude and phase.
d. Understand AC rms quantities and average power.
e. AC quantities can be described by phasors which have both magnitude and a rotating phase.
f. Phasor diagrams show the impedances and/or voltages across the elements of the circuit as
well as their relationship to the source voltage and the current.
g. ELI the ICEman. Positive reactance and phase (ELI). Negative reactance and phase (ICE).
h. Be familiar with the numerous relationships amongst the quantities: R, L, C, ν, ω, ω0, Vmax,
Vrms, Imax, Irms, Pmax, Pave, VL, VC, VR, Z, |Z|, X, XL, XC, φ. Given a few of these quantities,
be able to calculate all of the others!
7) Transformers
a. Ideal transformers have perfect flux transfer.
V
N
I
b. Fundamental equations: 2 = 2 = 1 , including power conservation.
V1 N 1 I 2
2
N 
c. Effective load: R ' = R 1 
 N2 
d. Know when it's convenient to use the currents vs voltages in calculations.