Page 314 - Engineering Electromagnetics, 8th Edition

296 ENGINEERING ELECTROMAGNETICS

We may summarize the use of the potentials by stating that a knowledge of the
distribution of ρ ν and J throughout space theoretically enables us to determine V and
A from (57) and (58). The electric and magnetic fields are then obtained by applying
(50) and (51). If the charge and current distributions are unknown, or reasonable
approximations cannot be made for them, these potentials usually offer no easier path
toward the solution than does the direct application of Maxwell’s equations.

8
D9.7. A point charge of 4 cos 10 πt µCis located at P + (0, 0, 1.5), whereas
8
−4 cos 10 πt µCisat P − (0, 0, −1.5), both in free space. Find V at P(r = 450,
θ, φ = 0) at t = 15 ns for θ =:(a)0 ;(b)90 ;(c)45 .
◦
◦
◦
Ans. 159.8 V; 0; 143 V
REFERENCES
1. Bewley, L. V. Flux Linkages and Electromagnetic Induction.New York: Macmillan,
1952. This little book discusses many of the paradoxical examples involving induced (?)
voltages.
2. Faraday, M. Experimental Researches in Electricity. London: B. Quaritch, 1839, 1855.
Very interesting reading of early scientific research. A more recent and available source
is Great Books of the Western World, vol. 45, Encyclopaedia Britannica, Inc., Chicago,
1952.
3. Halliday, D., R. Resnick, and J. Walker. Fundamentals of Physics. 5th ed. New York:
John Wiley & Sons, 1997. This text is widely used in the first university-level course in
physics.
4. Harman, W. W. Fundamentals of Electronic Motion.New York: McGraw-Hill, 1953.
Relativistic effects are discussed in a clear and interesting manner.
5. Nussbaum, A. Electromagnetic Theory for Engineers and Scientists. Englewood Cliffs,
N.J.: Prentice-Hall, 1965. See the rocket-generator example beginning on p. 211.
6. Owen, G. E. Electromagnetic Theory. Boston: Allyn and Bacon, 1963. Faraday’s law is
discussed in terms of the frame of reference in Chapter 8.
7. Panofsky, W. K. H., and M. Phillips. Classical Electricity and Magnetism.2ded.
Reading, Mass.: Addison-Wesley, 1962. Relativity is treated at a moderately advanced
level in Chapter 15.

CHAPTER 9 PROBLEMS
9.1 In Figure 9.4, let B = 0.2 cos 120πt T, and assume that the conductor
joining the two ends of the resistor is perfect. It may be assumed that the
magnetic field produced by I(t)isnegligible. Find (a) V ab (t); (b) I(t).
9.2 In the example described by Figure 9.1, replace the constant magnetic flux
density by the time-varying quantity B = B 0 sin ωt a z . Assume that U is
constant and that the displacement y of the bar is zero at t = 0. Find the emf
at any time, t.