Page 288 - Engineering Electromagnetics, 8th Edition

270 ENGINEERING ELECTROMAGNETICS

D8.13. A solenoid is 50 cm long, 2 cm in diameter, and contains 1500 turns.
The cylindrical core has a diameter of 2 cm and a relative permeability of 75.
This coil is coaxial with a second solenoid, also 50 cm long, but with a 3 cm
diameter and 1200 turns. Calculate: (a) L for the inner solenoid; (b) L for the
outer solenoid; (c) M between the two solenoids.

Ans. 133.2 mH; 192 mH; 106.6 mH

REFERENCES
1. Kraus, J. D., and D. A. Fleisch. (See References for Chapter 3.) Examples of the
calculation of inductance are given on pp. 99–108.
2. Matsch, L. W. (See References for Chapter 6.) Chapter 3 is devoted to magnetic circuits
and ferromagnetic materials.
3. Paul, C. R., K. W. Whites, and S. Y. Nasar. (See References for Chapter 7.) Magnetic
circuits, including those with permanent magnets, are discussed on pp. 263–70.

CHAPTER 8 PROBLEMS

8.1 A point charge, Q =−0.3 µC and m = 3 × 10 −16 kg, is moving through
the field E = 30a z V/m. Use Eq. (1) and Newton’s laws to develop the
appropriate differential equations and solve them, subject to the initial
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conditions at t = 0, v = 3 × 10 a x m/s at the origin. At t = 3 µs, find (a) the
position P(x, y, z)of the charge; (b) the velocity v;(c) the kinetic energy of
the charge.
8.2 Compare the magnitudes of the electric and magnetic forces on an electron
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that has attained a velocity of 10 m/s. Assume an electric field intensity of
5
10 V/m, and a magnetic flux density associated with that of the Earth’s
magnetic field in temperate latitudes, 0.5 gauss.
8.3 A point charge for which Q = 2 × 10 −16 C and m = 5 × 10 −26 kg is moving
in the combined fields E = 100a x − 200a y + 300a z V/m and B =−3a x +
2a y − a z mT. If the charge velocity at t = 0is v(0) = (2a x − 3a y −
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4a z )10 m/s (a)give the unit vector showing the direction in which the
charge is accelerating at t = 0; (b) find the kinetic energy of the charge at
t = 0.
8.4 Show that a charged particle in a uniform magnetic field describes a circular
orbit with an orbital period that is independent of the radius. Find the
relationship between the angular velocity and magnetic flux density for an
electron (the cyclotron frequency).
8.5 A rectangular loop of wire in free space joins point A(1, 0, 1) to point
B(3, 0, 1) to point C(3, 0, 4) to point D(1, 0, 4) to point A. The wire carries a