William H. Hayt and John. A. Buck, Engineering Electromagnetics. McGraw-Hill, ver 7, 2006.
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5.7. Assuming that there is no transformation of mass to energy or vice-versa, it is possible to
write a continuity equation for mass.
a) If we use the continuity equation for charge as our model, what quantities correspond to J
and ρv? These would be, respectively, mass flux density in (kg/m2 − s) and mass density
b) Given a cube 1 cm on a side, experimental data show that the rates at which mass is
leaving each of the six faces are 10.25, -9.85, 1.75, -2.00, -4.05, and 4.45 mg/s. If we
assume that the cube is an incremental volume element, determine an approximate value
for the time rate of change of density at its center. We may write the continuity equation
for mass as follows, also invoking the divergence theorem:
5.8. The conductivity of carbon is about 3 × 104 S/m.
a) What size and shape sample of carbon has a conductance of 3 × 104 S? We know that
the conductance is G = σA/, where A is the cross-sectional area and is the length. To
make G = σ, we may use any regular shape whose length is equal to its area. Examples
include a square sheet of dimensions × , and of unit thickness (where conductance is
measured end-to-end), a block of square cross-section, having length , and with crosssection
dimensions √ × √, or a solid cylinder of length and radius a =
b) What is the conductance if every dimension of the sample found in part a is halved?
In all three cases mentioned in part a, the conductance is one-half the original value if
all dimensions are reduced by one-half. This is easily shown using the given formula for
5.9a. Using data tabulated in Appendix C, calculate the required diameter for a 2-m long nichrome
wire that will dissipate an average power of 450 W when 120 V rms at 60 Hz is applied to it:
The required resistance will be