Additional Problems for
Electricity, Magnetism, and Thermodynamics
Dan Styer
May 2009
The letters HRW7 refer to the text by D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics,
seventh edition (John Wiley, New York, 2005), while HRW8 refers to
A changing magnetic eld makes an electric eld. A changing electric eld makes a magnetic eld.
These phenomena are expressed mathematically through the Faraday law and the Ampere-Maxwell law:
Ed =
dB
dt
and
Bd = 0
0
dE
dt
(1)
As an example, consider an inn
Analogy between electric and uid circuits
Dan Styer
A simple circuit
Electric circuit
i
i
E
i
R
i
Water flow circuit
plateau
rapid
pump
low-level flatland
electric current (Coulombs/sec.)
emf device
resistor
electric force
non-electric force of emf device
Solution of the RC circuit dierential equation
ODE:
ansatz:
dq(t) q(t)
Em
+
=
sin(t)
dt
RC
R
q(t) = Q cos(t )
(1)
(2)
where the Q and are adjustable parameters that will depend (in ways to be uncovered) upon R, C, , and
Em .
Plug the ansatz into the ODE,